No. God is not composed of matter and form. There is no matter in God because matter is potentiality, whereas God is Pure Actuality (as we demonstrated in Q2 A3).
Form perfects matter, because matter participates the form. But God is the essential good prior to any participated good.
Every agent acts by its form. God is First Agent because He is of His essence a form.
Thus God cannot be a composite being composed of the correlative principles of matter and form.