Well, first things first, the concept of a "nation" wouldn't exist until some 300 years after the fall of the byzantine empire, along with the concept of "ethnicity". Separatism on the grounds of ethnicity, aka nationalism, was unheard of in the medieval period.

Second, no Byzantines in Greece would have considered themselves Greek, at least not until the very late period. The Byzantines, including those in Greece, were christian Romans (you may not think of them as such, but that's definitely what they thought of themselves), and they didn't see much of themselves in the pagan Greeks. In fact, they were so far removed from the traditional Greeks that the word "Greek" was an insult meaning pagan. Geographical greeks would have roughly the same culture and identity as geographical anatolians, thracians, and ponts.

There would be no desire whatsoever to secede from the empire in Greece, though if the ruling emperor was doing a bad job they would try to replace him.

Third, "greece" as an area was very small, poor, and underpopulated. In the ancient and medieval periods, "greece" was about half the size of what we consider greece. It was roughly the same area as the southern half of modern greece, and made up around 1/12th (maybe less) of the empire's population in 950 ad. Even if there was separatist sentiment in greece, it would never be able to raise enough troops to secede.

TLDR: no, and there was no reason for there to be any