Turkification was a long drawn out process that wasn't really completed until the 20th century. Though it should be noted that a large part of the early Ottoman army was made of Greeks and Armenians who converted to Islam.
And on another note when you compare the genetics of modern Turks and Greeks, they share many haplogroups with each other.
Very true. Though it's worth noting that in some parts of Anatolia, Turkification was already completed by the early 1500s at the very latest, even if a lot of the Turks there were actually mixed Turko-Romans:
Maps on the Web
Religion in five Ottoman provinces in Anatolia according to the 1520s Ottoman hearth census: 92% Muslim, 7.9% Christian. by Lithide: The Christian proportion of Anatolia actually rose in the sixteenth...
mapsontheweb.zoom-maps.com
Anyway:
'AHC: Additional realistic US colonial acquisitions other than the Danish West Indies in a no-World Wars TL'