So assuming God had unlimited computing power, would He always win or draw?
Yes, with the usual caveat: that's a big if. Infinity is not part of usual computational discussions.
But yes, with true infinite computing power (i.e., well outside the scope of what reality can offer), any pure strategy, no-hidden-info, 2-player game can theoretically be "solved".
And, if solved, it is pretty much agreed that white has no deficit in chess that would meanlead to black wins the solved gamebeing able to force a win for black. The best black can hope for is a draw. White should at least be able to force a draw (if not win).