Mostly what Elfwine is saying. Crusaders likely can't take Egypt, and Byzantines are far from guaranteed as long as Alexios III is on the throne. Honestly I would not be surprised at all if Alexios is usurped even without the crusade. The only question is by whom. Obviously OTL's Alexios IV is a possibility, but also Theodore Laskaris, the Komnenoi, hell, basically any of the men who formed their own states during or after the OTL fourth crusade were in a position to potentially usurp the throne, and all of them have claims as good or better then Alexios III himself's on the throne.
In short the Romans are going to be in dire straits for at least a generation unless they get extremely lucky and one of the contenders totally dominates the others without much damage in the inevitable civil war that comes, and the Crusaders, while they might well retake Jerusalem, and even could possibly break the strength of the Ayyubids or topple their dynasty, taking control of any large portion of Egypt just isn't in the cards for them.
In short the Romans are going to be in dire straits for at least a generation unless they get extremely lucky and one of the contenders totally dominates the others without much damage in the inevitable civil war that comes, and the Crusaders, while they might well retake Jerusalem, and even could possibly break the strength of the Ayyubids or topple their dynasty, taking control of any large portion of Egypt just isn't in the cards for them.