Actually, I should be more clear. Let T = theism, H = theism makes people happier, L = lots of people are theists. Then H&L are evidence for T iff the quotient P(H&L|T)/P(H&L|~T) > 1. We can rewrite this quotient as P(L|H&T)/P(L|H&~T) * P(H|T)/P(~H|T). Then the thread-starter's argument at best shows that T is irrelevant to L once we know H, hence P(L|H&T)/P(L|H&~T) = 1. So in this best-case scenario, the quotient becomes P(H|T)/P(H|~T). If theists can show this is greater than 1, then H&L still ends up as evidence for theism. So that's what you really have to be asking.