No doubt there is plenty of mixed blood - that always follows this kind of conquest - but they are still a distinct ethnic group, and no self-respecting Greek or Armenian would claim ethnic commonality, either as a matter of genetics or of character.
of course, neither would admit that they are related to the the other, but I'm pretty sure that by blood the people in Turkey are mostly NOT Turkic. Even if you look at their features (not the most scientific of methods I'll agree) -- they look the same as the other Indo-Europeans/Caucasian people in that area and look nothing like the Kazakhs, Turkmen etc.
Character is also determined by culture, not genetics