No, Hawking wasn't saying that at all. Hawking was a theoretical physicist, not a philosopher or a theologian. Hawking meant to say exactly what he did say and that is what he said in his book "The Grand Design" and elsewhere. The universe can exist with the need of a supernatural "First Mover."
I don't know if Hawking agrees with your theory or not because he has never said anything about it.
I am not saying that your idea is a bad idea, just that you can not attribute it to Hawking.