Saying all of this as a Grecophile...
Honestly, it's nearly impossible for Greece to win the Greco-Turkish war without massive assistance from Britain, France, or another great power. Greece has to fight through deeply hostile territory, with stretched supply lines and finances, if it wants to force a favorable peace deal. Killing Ataturk doesn't really make that any more possible, though it could certainly prolong the struggle.
If, however, Greece does win the war, they're probably not going to gain Constantinople. None of the powers at large were interested in seeing the city ceded to Greece, and unless keeping it under international control becomes unviable or Greece annexes all of the territory around the Bosphorus, it isn't going to happen.
As for the effects of them winning, they aren't good. The Greek state is going have a hard time properly administrating any new territory that they gain, especially if it's full of a hostile population. Population exchanges are an option, but unlike OTL they're now going to have territory that's majority Turkish (Constantinople, Ionia, other regions typically in a Greek-wank map) which means millions of more people to deport along with destroying the economic value of their newly conquered territory. All this is just a recipe for disaster, and further bloodshed between the two down the line.