I do think a renewed interest in things Greek would be a good thing for education in all the Western world and possibly in Greece.
Specially if the Romaic Empire (aka Byzantine) was put in its proper place in history.
But not the Romaic Empire only. The Frank-Germanic tribes as well. I believe the impact of the events from the 8th to 14th century are deeply misunderstood in modern historiography.
The Romaic Empire was indeed the Roman Empire, Christianized and Hellenized. Was it different from the Pagan Roman Empire? Of course, but no less then modern Spain is from old Iberia. The Spanish and Portuguese *are* the Iberians. Since Constantine moved culture, state and even people (therefore DNA) to Constantinople, they were the Romans.
Now, were the Westerns Romans, despite being Frank-Germanic? In a sense yes, and in way that Rome itself had created by expanding Roman citizenship to those who were not born in the city. Western Romanity *is* a way of being Roman that was created and sanctioned by Rome itself. It is a romanity based on the concept of foederatti.
In fact, the chasm between Romaic romanity and Western romanity reflects the born citizen / naturalized citizen dichotomy. Interestingly enough, actual Romans, people born in the city of Rome, couldn't care less about all this. Only the descedants of the exiled Romans and of the naturalized Romans were concerned about their identities, and that is an expression of a verified social phenomena: that "branches" of a certain culture are usually more conservative about it then the original culture. Thus settlers and colonizers were usually more conservative about their culture and language then the ones in the metropolis. Also, naturalized citizens tend to "overplay" a stereotype of that culture, at least for sometime, before they get "natural".
Obviously, although they were "exiled romans" and "naturalized romans" they were both romans in a sense. But, and this makes a great difference, the fall of the Roman Empire did cause a cultural rupture that left the naturalized romans to do much guess work about what being Roman meant. Also, they lost the international language of culture and philosophy that was Greek, and even the literacy in Latin, while their ethnic languages didn't even have a consolidated written form. That's another serious rupture. The Romaic Empire, on the other hand, had much higher standards of culture preservation, even in its lower periods. That means that they could know better what being a Roman meant, what being a Christian meant, as well as be able to continually develop the form of their language without ever loosing contact with the registered insight of previous generations. Much of the emphasys on the Pope came, in my opinion, from a quiet desperation with the loss of this natural authority that History provides in the contact with Tradition. With no solid past to support the present and future, a figure of authority had to be produced.
Anyways, I think that studying Greek history, specially from the Romaic period on (that is, since the foundation of Constantinople, including the complete hellenization of the Roman Empire, a trend that existed since the foundation of the city itself), can provide us Westerns with deep, fruitful insights about our own history as cultural descedants of those "naturalized Romans" who were once called barbaric tribes.