No. God is not classifiable as a species of any genus because God is Pure Act, whereas the actuality of a specific difference is required to differentiate the potentiality of a genus.
Neither is God the purported genus "being". True, His existence is His essence, but as Aristotle demonstrated in the Metaphysics, being cannot be a genus.
Because His essence does not differ from His existence, there can be no definition of God. As the principle of all being, He cannot be classified by any genus.