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Pax, Baptism as we know has replaced Circuмcision. Circuмcision left its mark on the body. The Doctors and Saints say, mostly in expressing the non-repeatability of Sacramental Baptism, that Baptism likewise leaves its indelible mark on the soul. It also makes us full members of the Mystical Body. Some here have speculated that BOD would have to impress the Sacramental Character also. I hold that Cornelius received BOD, as I explained with sources from Scripture and Tradition (like St. Augustine and the Council of Orange - that's now the sixth ancient source on BOD by my count that comes to mind), but if he had received the Character then, what need for him to be baptized? In fact, he could not have been. I hold that in Water Baptism, one receives the plenary remission of all temporary punishments including those which, depending on the intensity of one's contrition, one would not have been released from in BOD, as St. Thomas and St. Alphonsus explain. Thus, even one who has already received BOD still needs to be baptized to be able to go to Heaven straightaway rather to Purgatory. The Character of Sacramental also makes us full members of the Visible Body of the Church.

Here's the text of St. Ambrose as cited by Mirari Vos: “Or if the fact disturbs you that the mysteries have not been solemnly celebrated, then you should realize that not even martyrs are crowned if they are catechumens, for they are not crowned if they are not initiated.  But if they are washed in their own blood, his piety and his desire have washed him, also.”

I'm not sure what St. Ambrose means by the first sentence. The second seems fairly plain. St. Ambrose is arguing from the fact that almost everyone grants that Martyrs are saved, because they are washed in their own blood. Thus, the Doctor is saying, similarly, the Catechumen is washed by his piety and desire (what St. Augustine, cited by St. Thomas had called "faith and conversion of heart".)

Regarding the first sentence, could it possibly refer to Baptism and Confirmation/Chrismation? I don't know. Maybe St. Ambrose meant "they are not Crowned/Chrismated" if they are not "Initiated/Baptized". Thus the meaning would be martyrs who are catechumens are neither Baptized nor Chrismated. Maybe. But I'm not sure what it means and I haven't really meditated on that part of the text before. 

Question to you: Someone who dies justified has Christ and the Holy Spirit living in him. Can he really go to hell/limbo for all eternity?

The opinion that someone is lost who dies in Grace, who merited eternal life by the good works he did in God, as Trent said, is heretical.

There is no dogmatic Tradition of adults going to limbo now in the era after Christ. Supposing they did go to limbo, which limbo?

The limbo of the Fathers? But that is closed. Second, if supposedly they could go there, then could they supposedly leave also one day?

The limbo of the infants? But they are not infants. Moreover, justification means the remission of original sin. So they don't have OS.

The Old dispensation was different. Yet, even in the OT, those who died in Grace were ultimately saved. They just had to wait.

God not only foreknew but also predestined all His elect would die in Grace. And He has determined that that is sufficient for salvation.