No, no one can be saved without the Catholic Faith. This truth is itself an object of the Catholic Faith, is irreformable and dogmatically definable, is contained in innumerable Creeds, ( “Iniunctum nobis,” Pope Pius IV, “This true Catholic Faith, outside of which no one can be saved… I now profess and truly hold…", Nuper ad nos, Pope Benedict XIV, , March 16, 1743, Profession of Faith: “This Faith of the Catholic Church, without which no one can be saved, and which of my own accord I now profess and truly hold…”) taken by Roman Pontiffs with the greatest solemnity in public professions of the Faith, which it is the duty of St. Peter and his perpetual successors to guard.
“Q. Whether a minister is bound, before baptism is conferred on an adult, to explain to him all the mysteries of our Faith, especially if he is at the point of death, because this might disturb his mind. Or, whether it is sufficient, if the one at the point of death will promise that when he recovers from the illness, he will take care to be instructed, so that he might put into practice what has been commanded him.
“A. A promise is not sufficient, but a missionary is bound to explain to an adult, even a dying one who is not entirely incapacitated, the mysteries of Faith which are necessary by a necessity of means, as are especially the mysteries of the Trinity and the Incarnation.”
Not even the express will to be Catholic therefore suffices when the intellect is ignorant or unenlightened about the primary mysteries of Faith necessary by a necessity of means, without which no one attains the beatific vision. No soul will ever enjoy the inexpressible bliss that comes from the sight of the Triune God in eternity unless in this life she has known and loved God one and Triune, and recognized the Lord Jesus Christ as the Incarnate Son of God and the sole Redeemer of the whole human race.
Pope St. Pius X informs us,
"We declare that a great number of those who are condemned to eternal punishment suffer that everlasting calamity because of ignorance of those mysteries of Faith which must be known and believed in order to be numbered among the elect."
Fr. Mueller explains the teaching of all Tradition and the Church below, as do St. Thomas and St. Alphonsus, on how those in invincible ignorance and implicit faith, if they but persevere in doing what lies in their power with the help of actual grace that God gives them to know and believe the Truth by which they might be saved.
Q. What are we to think of the salvation of those who are out of the pale of the Church without any fault of theirs, and who never had any opportunity of knowing better?
A. Their inculpable ignorance will not save them; but if they fear God and live up to their conscience, God, in His infinite mercy, will furnish them with the necessary means of salvation, even so as to send, if needed, an angel to instruct them in the Catholic Faith, rather than let them perish through inculpable ignorance.
The text above has ecclesiastical and Roman approbation, including from the Sacred Congregation for the Propagation of the Faith. Fr. Michael Mueller, CSSR, who lived about a 100 years ago, was a true son of St. Alphonsus, as I will prove shortly, and his burning, fervent and lifelong desire ever since he landed on her shores, was to see America become Catholic. That is part of the reason he combated those who were teaching souls can be saved without the Catholic Faith, he and a friend of his, by the grace of God, bought thousands of souls to Christ and His Church.
we answer the Semipelagians, and say, that infidels who arrive at the use of reason, and are not converted to the Faith, cannot be excused ... St. Thomas explains it, when he says, that if anyone was brought up in the wilds, or even among brute beasts, and if he followed the law of natural reason, to desire what is good, and to avoid what is wicked, we should certainly believe either that God, by an internal inspiration, would reveal to him what he should believe, or would send someone to preach the Faith to him, as he sent Peter to Cornelius.
Thus, then, according to the Angelic Doctor, God, at least remotely, gives to infidels, who have the use of reason, sufficient grace to obtain salvation, and this grace consists in a certain instruction of the mind, and in a movement of the will, to observe the natural law; and if the infidel cooperates with this movement, observing the precepts of the law of nature, and abstaining from grievous sins, he will certainly receive, through the merits of Jesus Christ, the grace proximately sufficient to embrace the Faith, and save his soul.”
This teaching is irreformable and definable, and in the wake of the Conciliar revolution, it acquires greater importance than it had a 100 or so years ago. If this teaching were solemnly reaffirmed tomorrow, it would be the beginning of the end of the Conciliar revolt against Catholic Tradition. Anyway, in the meanwhile, it is also contained in the infallible Athanasian Creed, and is the teaching of the Holy Bible and of all the Fathers, of all Sacred Scripture and of all Sacred Tradition from the very beginning of the Church, as even its few opponents admit (St. Alphonsus relates concerning the few who first began in the 16th and 17th centuries to seriously propose the novel opinion that a man might somewhere, somehow happen to be saved without the Catholic Faith, "They respond that even though all the Scriptures and Holy Fathers’ testimonies oppose this opinion, their opinion is more easily explained by necessity of precept, or because ordinarily almost none are saved without explicit faith in the mysteries") and should consequently be regarded by all traditional Catholics, who wish to hold to what the Church has always and everywhere held, as entirely beyond doubt and absolutely certain.
“Whoever wishes to be saved, needs above all to hold the Catholic Faith; unless each one preserves this whole and inviolate, he will without a doubt perish in eternity. Now, the Catholic Faith is this, that we worship one God in the Trinity, and the Trinity in unity…But it is necessary for eternal salvation that he faithfully believe also in the incarnation of our Lord Jesus Christ…the Son of God is God and man… This is the Catholic Faith; unless each one believes this faithfully and firmly, he cannot be saved.”