I've got my doubts it'll give birth to a new Roman identity, but the whole "True Roman Empire" thing might become even more important to the modern greek identity. While Greeks under the Ottoman empire retained some sense of being Rhomanoi, they had been presenting themselves as "Hellenes" for some time, and had even used it to capitalize on western sympathies during their struggle for independence. At this point, there was already a new sense of the Greek nation and Greek nationalism, with Byzantium as an important part of its past, and the Megali Idea as it's destiny to take back it's rightful lands. Actually! there's a lovely little story; on the Island of Lemnos in 1912, when the Turkish garrison occupying it were dispelled by Greek soldiers, Children came out to examine them. When asked why they were so curious, they said they wanted to see what "Hellenes" looked like, the soldiers responded "are you not Hellenes?" and they responded in turn "No, we are Romans". I found that quite interesting, that on one isolated island the Roman national identity managed to last up to 1912.
In any case, I often find myself wondering HOW the Greeks managed to botch this war up so bad, but it's not my point of expertise. One things for sure, I can't see them holding onto that much of the pontic coast, I imagine if they do very well they might be able to keep a reduced section of the Aegean coast (the Greek majority areas), Thrace and Constantinople, but other then that it's biting off way more then they can chew.