Maybe.
But maybe all Bush, or someone like him, would do is throw them a bone. Then, the religionists go off half-cocked thinking power is on their side. In hierarchical human societies the political leader was also often the spiritual leader. Sometime, circa 5000 years ago there was a fat, grass skirt-wearing chieftain dude with a shark-tooth necklace who everyone referred to as God, and it stuck.
Religion is like science fiction. It presents a set of rules, some fictitious, that people use to decide right from wrong. True believers fail to questions the rules, and then apply them in as many ways as they can imagine or come up with. It's extrapolation at its worst.
