I wouldn't call it as much a last stand as a slow, painful drowning, but yes, the Byzantines held out much longer than anybody would have thought. Especially after being partitioned.......But the Ottomans, in my opinion, are the third Rome. Just because Islam is not the religion of the time in Europe doesn't make them not the Third Rome. The way of life of the people in Constantinople/Istanbul was much more European than Central Asian/Arab/Other type of denomination for Turks. As I consider Byzantines=Romans, but Romans at their lowest point, I think that continuity should be observed and whatever Western historians call Eastern Rome be damned.
But the Ottomans are WAY more important than the Byzantines/Eastern Romans had been since the reign of Basil II, debatably the last time the Byzantines where powerful. Since I know Fireaxis will split Rome, I'll consider any period post the reign of Justinian the Byzantines for what I'm going to say. Justinian spoke Latin, later emperors spoke Greek. So if Fireaxis splits Rome, then the Byzantines are DEFINETLY less important than the Ottomans, if not, I'll be happy to see both appear(Romans/Ottomans, not Byzantines/Romans)