Yes, as above, I can imagine a Greek-speaking Orthodox Christian rump state, possibly in modern OTL Greece, which has some kind of political continuity - possibly ruled by a major Byzantine noble family, which the Ottomans don’t bother to conquer properly, but I can’t imagine the Ottomans passing up on a city which was already known in all of the surrounding languages as just “The City”, and I can’t imagine the Ottomans tolerating a surviving rump state that still claims to be The Roman Empire for long if they can do anything about it. I think it’s also as above possible to imagine some kind of Trebizond surviving, though not the one that existed in the mid-15th century OTL.
I could imagine this Byzantine rump-state in Greece eventually becoming revived like the other Orthodox Christian states in the Balkans, but I think that the consequences aren’t necessarily physically that different from Greek independence OTL; what it does possibly mean, though, is that because there is a state continuity going back to that degree, you could end up with modern *Greece that identifies itself as being Romania and its people as Romans, instead of what we got OTL, wherein they self-identified as Hellas and its people as Hellenes, wherein the early Greek nationalists emphasized their antique predecessors rather than their medieval ones.
What does make it more unlikely I think is that part of the reason you had the rump states in the Balkans was because that territory was constantly contested by the Hungarians, Austrians, Polish-Lithuanians and, later, the Russians; the Ottomans weren’t able to establish consistent control in those regions. I think, to have a rump Roman state, you need to have - oddly enough - both a stronger and a weaker Ottoman Empire. One that‘s strong enough to take Constantinople a bit sooner, but weak enough that it can’t fully express its authority in OTL Greece and/or Trebizond.