Well, Age of Miracles convinced me that it could survive a post-Fourth Crusade scenario...granted, I have little love for the Palaiologos dynasty in general, sans maybe Michael VIII and Constantine XI (albeit for more of a BotW reason than anything...)
Still, even with a 1356 scenario, it is stretching plausibility a bit, but even then, history has seen a lot of weird things that happened, and the fact that Byzantium even survived to 1453 was a stretch in plausibility, even by historical scenarios...I'm pretty sure you would have to agree with me on that Elfwine.
You do realize it being a stretch that they got as far as they did otl kind of works against the argument that they could go for a hundred and fifty more years. I mean maybe a decade at most, but frankly their end would probably only be more pathetic than it was OTL (although to be fair OTL was about as dignified an end as the Roman Empire could ever receive. I mean it works much better as a better story to have a gallant last stand against impossible odds than to have them be brought down in pathetic whimpering sackings).