Except Trent doesn't have a "ne" or "neque" before "avail."
No, but the sense is the equivalent. Ne is not strictly required to have the same sense. One clue would be whether the verb is in the subjunctive mood. What's key is that St. Fulgentius uses the same concept (we'll have to see if it's the same Latin verb) without it necessary implying that it's sufficient in and of itself for salvation, rather sufficient for salvation in the sense of being sufficient to insure reception of the Sacrament.
He said that confession "avails" for salvation. Right?
But HOW does it avail? It avails by insuring reception of the Sacrament.