There's zero chance. First, Istanbul was the hardest city in the world to seige before the tank. Remember how Galllipoli went? And meaning it took the biggest possible budget need to waste.
And everybody, especially Russia, wanted the city themselves.
If the allied forces are willing to go that far as to attack Constantinople for Greece,I have no doubt they would turn the city over to the Greeks.Obviously,the great powers wouldn't be willing to turn the city over to any one of them,but an exception can always be made to a minor power with a historic claim to the city.
As for Constantinople being the hardest city in the world to attack before the tank,this is completely false.This is the 19th century remember and the Ottoman forces are fairly archaic compared to the allied forces and still in the midst of reform. Besides that,no one is going to land in Gallipoli.The Russians are probably going to march their armies around the Black Sea Coast,down Romania and Bulgaria and then attack the city.IIRC,the defences around Constantinople are fairly archaic.