Absolutely not! God's Word is very clear that such a possibility simply does not exist.
First of all, let us remember that God made animals and humans according to their kind (Genesis 1:21, 24-28). Animals can only reproduce other animals, according to their kind (two dogs can produce another dog, but they can't produce a horse or a bird), and men can only produce humans (they can't produce animals). Since men and angels belong to a different "kind," it is impossible for that reason alone, that they could produce human offspring.
The question of God's omnipresence has puzzled men for centuries and millennia, and diverse and sometimes incredible answers have been proposed.
One common idea in Orthodox Christianity is that God, as a Spirit being, is everywhere, as allegedly, Spirit has no form or shape--no limitations--no "parts." God is understood to be--even though proponents of that idea would oppose such wording--a formless or shapeless "blob"--permeating everything.
"You are the light of the world. A city that is set on a hill cannot be hidden."
-Matthew 5:14