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Regarding the quote above, Judas was never baptized.

355.

The Redeemer of the world, departing from Jerusalem and traveling about in Judea for some time, pursued the work of preaching and performing miracles. While He was baptizing and at the same time commissioning his disciples to baptize, as is recorded in the third and fourth chapter of Saint John’s Gospel, his Precursor also continued to baptize in Ainon on the banks of the Jordan near the city of Salem. But the Baptisms of the Lord and those of saint John were not of the same kind: for saint John continued to give only the baptism of water and of penance, while our Lord administered his own Baptism, that of real pardon of sins and justification, such as it is now in the Church, accompanied by the infusion of grace and of the virtues. To the mysterious power and effects of the Baptism of Christ was moreover added the efficacy of his words and instructions confirmed by the wonder of his miracles. On this account more disciples and followers soon gathered around Christ than around saint John, in fulfillment of the words of the Baptist, that Christ must grow, while he must be diminished (John 3, 22). At the Baptisms of the Lord his most holy Mother ordinarily was present and She beheld all the great results of this regeneration in the favored souls.

375.

Judas was attracted to the school of Christ our Teacher by his forceful doctrines, and was filled with the same good intentions which moved the others. Powerfully drawn by these motives, he asked the Savior to admit him among his disciples, and the Savior received him with the bowels of a loving Father, who rejects none that come to Him in search of truth. In the beginning Judas merited special favors and forged ahead of some of the other disciples, deserving to be numbered among the twelve Apostles; for the Savior loved his soul according to its present state of grace and his good works, just as He did the others. The Mother of grace and mercy observed the same course with him, although by her infused knowledge She immediately became aware of the perfidious treachery with which he was to end his apostolate.

She did not, on this account, deny him her intercession and maternal love; but she applied Herself even more zealously to justify as far as possible the cause of her divine Son against this perfidious and unfortunate man, in order that his wickedness, as soon as it should be put into action, might not have the shadow of an excuse before men. Well knowing that such a character as his could not be overcome by rigor, but would only be driven by it to so much the greater obstinacy, the most prudent Lady took care, that none of the wants or the comforts of Judas should be ignored and She began to treat him, speak and listen to him more gently and lovingly than to all the rest. This She carried so far, that Judas, when the disciples once disputed among themselves concerning their standing with the Queen (as, according to the Evangelist [Luke 22, 24], it happened also concerning the Redeemer), never experienced the least jealousy or doubt in this matter; for the blessed Lady in the beginning always distinguished him by tokens of special love and he, at that time, also showed himself thankful for these favors.

376.

But as Judas found little support in his natural disposition, and as the disciples, not being as yet confirmed in virtue and not as yet even in grace, were guilty of some human failings, the imprudent man began to compliment himself on his perfection and to take more notice of the faults of his brethren than of his own (Luke 6,41). He permitted himself thus to be deceived, making no effort to amend or repent, he allowed the beam in his own eyes to grow while watching the splinters in the eyes of others. Complaining of their little faults and seeking, with more presumption than zeal, to correct the weaknesses of his brethren, he committed greater sins himself. Among the other Apostles he singled out saint John, looking upon him as an inter meddler and accusing him in his heart of ingratiating himself with the Master and his blessed Mother. The fact that he received so many special favors from Them was of no avail to deter him from this false assumption. Yet so far Judas had committed only venial sins and had not lost sanctifying grace. But they argued a very bad disposition, in which he willfully persevered. He had freely entertained a certain vain complacency in himself; this at once called into existence a certain amount of envy, which brought on a calumnious spirit and harshness in judging of the faults of his brethren. These sins opened the way for greater sins; for immediately the fervor of his devotion decreased, his charity toward God and men grew cold, and his interior light was lost and extinguished; he began to look upon the Apostles and upon the most holy Mother with a certain disgust and find little pleasure in their intercourse and their heavenly activity.

Mary Agreda described the youthful Lord as very serious and my remembrance was that she said that although He was extremely sweet and accommodating, He was quiet, somber, distant and detached to the point of concern/wonder for Our Lady and St. Joseph.  I doubt He played like other children because He was often in prayer and suffering from His birth. The crucifixion was the culmination of a life of suffering. Our Lord wasted no time on frivolity and lived a very austere life.  The depiction of Him playing like other little boys wasn't in character, at least according to Agreda.     

Judas could not have been baptized, since he committed ѕυιcιdє before Our Lord instituted the Sacrament of Baptism.  He may have received the baptism of St. John, that of repentance, but not the actual Sacrament of Baptism.

268.

When saint John had finished baptizing our Lord, the heavens opened and the Holy Ghost descended visibly in the form of a dove upon his head and the voice of his Father was heard: “This is my beloved Son, in whom I am well pleased” (Matth. 3, 17). Many of the bystanders heard this voice, namely, those who were not unworthy of such a wonderful favor; they also saw the Holy Ghost descending upon the Savior. This was the most convincing proof which could ever be given of the Divinity of the Savior, as well on the part of the Father, who acknowledged Him his Son, as also in regard to the nature of the testimony given; for without any reserve was Christ manifested as the true God, equal to his eternal Father in substance and in perfection. The Father himself wished to be the first to testify to the Divinity of Christ in order that by virtue of his testimony all the other witnesses might be ratified. There was also another mystery in this voice of the eternal Father: it was as it were a restoration of the honor of his Son before the world and a recompense for his having thus humiliated Himself by receiving the Baptism of the remission of sins, though He was entirely free from fault and never could have upon Him the guilt of sin (Heb. 7, 26).

269.

This act of humiliation in receiving Baptism in the company of those who were sinners, Christ our Redeemer offered up to the eternal Father as an act of acknowledgment of the inferiority of his human nature, which, in common with all the rest of the children of men, He had derived from Adam. By it He also instituted the sacrament of Baptism, which was to wash away the sins of the world through his merits. By thus humiliating Himself in this baptism of sins, He sought and obtained from the eternal Father a general pardon for all those who were to receive it; He freed them from the power of the demon and of sin, and regenerated them to a new existence, spiritual and supernatural as adopted sons of the Most High, brethren of their Redeemer and Lord. The past, present and future sins of men always remaining in the sight of the eternal Father, had prevented the effects of this Baptism; but Christ our Lord merited the application of this so easy and delightful remedy, so that the eternal Father was obliged to accept it in justice as a complete satisfaction according to all the requirements of his equity. Christ was also not deterred from thus securing this remedy by his foreknowledge of the abuse of holy Baptism by so many mortals in all ages and of its neglect by innumerable others. All these impediments and hindrances Christ our Lord removed by satisfying for their offenses, humiliating Himself and assuming the form of a sinner in his Baptism (Rom. 8, 3). This is the meaning of the words: suffer it to be so now for so it becometh us to fulfill all justice. Then in order to honor the incarnate Word and in recompense for his humiliation, and in order to approve of Baptism and establish its wonderful efficacy, the eternal Father gave forth his voice and the Holy Ghost descended. Thus was Christ proclaimed as the true Son of God, and all three Persons of the Holy Trinity ratified the sacramental rite of Baptism.

270.

The great Baptist was the one who reaped the greatest fruit from these wonders of holy Baptism; for he not only baptized his Redeemer and Master, saw the Holy Ghost and the celestial light descending upon the Lord together with innumerable angels, heard the voice of the Father and saw many other mysteries by divine revelation: but besides all this, he himself was baptized by the Redeemer. The Gospel indeed says no more than that he asked for it, but at the same time it also does not say that it was denied him; for, without a doubt, Christ after his own Baptism, conferred it also on his Precursor and Baptist. It was He that instituted this Sacrament afterwards as He made it a general law and enjoined the public ministration of it upon the Apostles after the Resurrection. As I shall relate later on, it was also the Lord who baptized his most holy Mother before its general promulgation, and He, on that occasion, established the form in which Baptism was to be administered. These facts were made known to me, and also that saint John was the first fruit of the Baptism of Christ our Lord and of the new Church, which He founded in this Sacrament. Through it the Baptist received the character of a Christian together with a great plenitude of grace, since he had not upon him original sin; for he had been justified by the Redeemer before he was born, as was said in its place. By the answer of the Savior: “Suffer it to be so now, that all justice be fulfilled,” He did not refuse, but He deferred saint John’s Baptism until He himself should have been baptized and have fulfilled the requirements of God’s justice. Immediately after his own Baptism He baptized saint John, gave him his blessing, and betook Himself to the desert.

319.

The most blessed Lady also asked Him for the Sacrament of Baptism, which He had now instituted, and which He had promised Her before. In order that this might be administered with a dignity becoming as well the Son as the Mother, an innumerable host of angelic spirits descended from heaven in visible forms. Attended by them, Christ himself baptized his purest Mother. Immediately the voice of the eternal Father was heard saying: “This is my beloved Daughter, in whom I take delight.” The incarnate Word said: “This is my Mother, much beloved, whom I have chosen and who will assist Me in all my works.” And the Holy Ghost added: “This is my Spouse, chosen among thousands.” The purest Lady felt and received such great and numerous effects of grace in her soul, that no human words can describe them; for She was exalted to new heights of grace and her holy soul was made resplendent with new and exquisite beauty of heaven. She received the characteristic token impressed by this Sacrament, namely, that of the children of Christ in his holy Church. In addition to the ordinary effects of this Sacrament (outside of the remission of sins, of which She stood in no need), She merited especial graces on account of the humility with which She submitted to this Sacrament of purification. By it She accuмulated blessings like to those of her divine Son, with only this difference: that She received an increase of grace, which was not possible in Christ. Thereupon the humble Mother broke out in .a canticle of praise with the holy angels, and prostrate before her divine Son, She thanked Him for the most efficacious graces She had received in this Sacrament.