Hard to say. It would certainly changes the post-Antioch Crusader politics, but eventually the emperor couldn't have gave forces to Crusaders up to the end (Attacking the Fatimid ally would be a really bad move from Alexios), and that would impact a lot its relationship with Latins.
The political situation isn't, surprisingly, really known and we can only trace some sides there.
Assuming this helps manage to make the Sieges of Antioch not only victories but quick and clear ones, Raimond IV would probably keep his political ascendency on the Crusade (especially maintaining domination over Tancrède and Robert II of Normandy) , with Alexios as (big) ally.
On the other hand, it wouldn't be that surprising to see Bohémond of Tarente simply going back in Italy, frustrated of conquering holdings there (maybe Sicilian Normands would take the place of Etienne of Blois ITTL in 1101?)
It's really likely that Alexios would manage to take Antioch for the Byzantines (while I'm less sure for Edessa, that would be already takenover. Not that he couldn't have besieged it, but it would have really provoked a clash with Crusaders).
Without Bohemond's presence in Antioch, Raimond would be less interested forging a principality in Syria and may eventually accept Jerusalem's kingship (or still refusing it, but maybe not creating the equivalent of the County of Tripoli, while still having a spiritual and political influence on the Kingdom of Jerusalem).
As it's unlikely Byzzies would continue after having fought Syrians and Turks, I don't really see much being taken over by Alexios pass the Oronte or at best modern Liban.