I was thinking about this very scenario today, and was considering fleshing out a timeline about it, though I am not sure where to begin or how to get the Turks to accept Christianity rather than Islam. If the Turks are Christianized, then this could mean successful Crusader States so assuming the Turks conquer Constantinople on schedule, it shouldnt be too hard to see the Levant and Palestine, and maybe even Egypt having a majority Christian population at the conquest of Byzantium, and becoming loyal provinces of the Empire. With the Christian Ottoman Empire as a bulwark in the East then perhaps we see a Catholic Reconquista of North Africa rather than colonialization of the Americas which is instead left to the British, Dutch, and Danes.