Sean, in order to understand what Trent is saying there, you need to read what Trent actually says there.
"And this translation, since the promulgation of the Gospel, [Justification] cannot be effected, without the laver of regeneration, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God".
"[Justification] cannot be effected, without the layer of regeneration, or the desire thereof" = "Justification can only be effected by the layer of regeneration,
or the desire [for the layer of regeneration: baptism]."
From the same chapter of Trent: "
Justification of the impious
is indicated, as being
a translation, from that state wherein man is born a child of the first Adam, to the state of grace."
The "state wherein man is born a child of the first Adam" clearly refers to Original Sin. Therefore, the text clearly says that justification removes the stain of Original Sin and puts someone in a state of grace. No one who perishes in a state of grace can be damned, that is de fide. So one who is justified is saved, by definition(note that the state of justification can be temporarily lost by way of mortal sin).
If one who is justified is saved, and justification can be effected by the
desire for baptism, as is taught by Trent, then one may be saved by desire for baptism.
I don't know how St. Alphonsus justifies implicit baptism of desire, but explicit BOD is strongly defended by Trent.