Admittedly, a more warring minded Greece would do much making Bulgaria joining Central Powers even more certainly than IOTL
Constantinople however, seems out of question. It was a strategic passage, the key to Russia. I don't see any great power giving the control to Greece (as I don't see Suez Canal being given as a token for good behavior).....
That is all logical and valid under ordinary diplomacy. It can all be chucked aside by a aggresive Greek leadership striking some sort of coup post WWI. Ataturks post 1919 government got away with a similar action due to the exhaustion of the Brits, French, and Italians, who one by one gave up on countering the Turkish fait accompli. If the Greeks were able to occupy the demilitarized zone surrounding the Sea of Marmarra a step ahead of the erstwhile Allies the other may find enforcing the treatys, or even writing them not worth the effort.