Will Greece ever recapture the New Rome from the Turks?
Greece never owned Constantinople, so it would not be a case of "recapturing" it but rather annexing it. What is now called Greece was part of the Roman Empire with Constantinople as its capital, so New Rome owned Greece, not the other way around.
A little known fact is that the Fall of Constantinople to the Ottomans coincided with a rise in Greek Nationalism led by the neoPlatonic philosopher Gemistus Pletho
. The new revival in "Greek nationalism" is no different, and it would be completely revisionist for it to claim that "Greece" ever "owned" Constantinople.
Let us not put the cart before the horse George.
It was Constantine he great who transformed the ancient Greek colony of Byzantium into a new imperial residence, Constantinople.