Eh...i think the old one did but last time i read the book (Dan Jurgens was on it, it was the "Dark Gods" arc, pretty good) he didnt, he didnt even have that whole human identity thing, just all god with his own power source as his divinity, not the hammer (tho it does always come back to him anyway).
Still, again, he's not the god he used to be, back when he had that Hulk power of immeasurable strength, but then again, it'dve been a bitch to beat the old godly superman too.
Hey, that might make another good fight.