specifically, the Christology of Islam comes from the Gnostics. I can't wait to see how the Gnostic gospels are really the foundation of (Sola Scriptura) Protestantism, but I am sure I will see it on this board.
An interesting study might concern the recent embracing of the Gnostic gospels by parts of our culture, and the inability of certain quarters (is there overlap?) to criticize Islam.
I think most of the inability to criticize Islam has to do with indoctrination in multiculturalism, where all cultures are "equally" valid, with a heavy dose of anti-Westernism. The successful have to get dragged down in order to level the playing field.
There is a certain amount of hollow emptiness in pure secularism & filling some of that with ancient or third world spirituality doesn't violate multiculturalism in the same way as embracing some of that old time religion dominant in ones own culture.
In short, I don't think it has to do with overlap, except in the broadest sense.