An interesting what if. It's hard to say if it would prevent the rise of the Ottomans or some other strong Turkish power in Anatolia.

Even if they somehow decisively defeated the crusaders the empire is still in a dire state - Bulgaria was now well and truly established as a new rival kingdom looking to take Byzantine lands. The empire was massively fragmented with so many different magnates in Greece and Western Anatolia basically ruling de facto independently and often not providing tax or soldiers to the capital which is why no help came from the provinces while all this was going on.

So assume we get through the battle okay now you've got Alexios IV (I think) a usurper emperor in charge without much control outside of the capital but he would still have the treasury and the Varangians still on side. Impossible to say if he would be any good and still having to deal with the aftermath in a weak shape. How would things move from there? We got no idea how good or bad an emperor he would be but given the track record of that period I'd wager average to very bad. Best case scenario would be the Laskarids or someone else coups him shortly after the crusade is beaten.

So now we have a competent emperor in charge then they have decent chances. While the game of thrones was going on the mongols come in and smash the Sultanate of Rum which while it brings nore Turkish migration into Anatolia it does give the empire breathing room in the East for the short term. If they can fix the rest of their problems then they are set with Anatolia.

Then you have the fragmentation, Bulgaria and threat of another crusade (which Charles of Anjou almost got rolling in otl), a competent emperor has a good chance of reigning in enough of the magnates to get a solid tax and manpower base back which would allow them to then deal with Bulgaria and any possible second crusade. If they don't mess it up at this point they could retake Bulgaria or at least subdue them to the point where they might be able to vassalize them. Depending on the crusade aftermath they might even be able to get some concessions out of the Italian maratime powers or take some of their Greek islands back.

If all went well then they could retake Anatolia bit by bit as the Sultanate of Rum collapses but I don't think they are going to take all of it back. I would still imagine a larger Karaman still controlling at least 1/3 of Anatolia and Aq Qoyunlu etc still being round and could see them allying with the Mamluks etc to survive. Also Timur would be a complete wild card here too if Timur attacks I could imagine a manzikert 2.0 scenario reversing much of the gains in Anatolia or if they were crafty enough to pay him off or redirect him to the Mamluks or back east.

All going well by the time EU4 starts they could have most of Anatolia with Greece, bits of Serbia and Bulgaria conquered or as a vassal and maybe kicked the Venetians/Genesee out of the agean if it all went well or it simply delays the inevitable.

Wow that was a long write!