I doubt it would have been for the better for the ERE
Anatolia is where most of its money came from
The most money were coming from custom dues in Constantinople, the biggest port at that time and probably the biggest trade hub in the "Mediterranean world".
A big part of Anatolia was sparsely populated and produced little: crusaders going through it had been suffering from shortages of food and fodder and excesses of a bad weather.
IMHO what most likely would happen is what happened after the Latin Empire - a rump centre, and successor states in Greece and the Balkans. These would be unable to come together and open to attack from the Muslim East
This more or less assumes that the Ottomans were inevitable, but were they, really? Their raise was a byproduct of (a) Mongolian defeat of the (already falling apart) Sultanate of Rum followed by (b) eventual fall of Il-Khanate with a complete disintegration of the Sultanate of Rum and (c) raise of the Osmans out of an obscure beylik to a major power thanks to creation of (anything but inevitable) innovative military system. With any of these factors going "wrong" that attack from Muslim East may not happen: the "Muslim East" was routinely engaged in the fights between various Muslim states.
The Latin Empire is a questionable parallel because it was a completely foreign entity in a region. And, rather ill-managed on the top of it.