I find it difficult to discuss topics like these, since there's absolutely no way to even predict what might happen if one crucial factor is eliminated from the course of history. However, when such predictions are made based on false facts, then I just might chime in for a response.
It is very clear that there would be independence movements in Byzantine Empire sooner or later, even if the Turks hadn't come to power. So the Turks factor aside, you absolutely cannot maintain the fact about a strong Byzantine Empire for unlimited period. Why? Coz it's stupid.

(Officialy, because it's not a factor; it's a condition and practically you're not predicting anything, you're imagining situations.)
Now, it's clear that Byzantine Empire would have fallen apart because it grew week from corruption inside, decentralization etc.
Also, it wasnt essentially Greek, but it was a mix of many different cultures. Plus there's the influx of Slavs around Vi century.
There were various kingdoms arising in Byzantia before the Turks. So, it would be the case again, even without them.
Also, a some form of Pretestant movement would have arisen, since Orthodoxy was just as corrupted as Catholicism. Actually, there have been such movements in the Middle Ages in Buzantia, but the arrival of the Turks in a way united the Christians there for the next centuries, to fight the common "religious infidels".
Another consequence could have been many more kingdoms arising during the Late Middle Ages, since there wouldn't be a strong Ottoman Empire to keep the country together, and the present countries would have formed much earlier. There would be no Islamic and Oriental influences in the Balkan cultures, as well as Anatolia, and Ionia would probably be Greek today.
And the thing you mentioned about the Hapsburgs, it is more likely they would have expanded in the Balkans more, since the Turks were the barrier that kept them from Northern Balkan for so long.
Or, if you dont like how I set the conditions, and would rather talk about a highly hypotetical situation of an everlasting strong Byzantine Empire, then my prediction is that it would conquer the world, and we would all be Orthodox today.