God appears, or disappears, in a puff of logic
I tried formalizing this argument, but it involved a lot of predicate logic, which I'm not super at, and am currently relearning. So here's the informal gist: If God exists, then God is active in the world. If God is active, then all evidence (i.e. all observation of the world) is God-caused (or at least God-approved). Conclusions from God-approved evidence are true (this is just a fundamental precept of religion). There exists evidence for evolution; therefore evidence for evolution is God-approved. Hence, evolution is a true conclusion.
Put it all together, with some identity substitutions and liberal use of the transitive property, and what do you get? "If God exists, then evolution is true." Now here's where things get interesting. A statement of the form A -> B (if A then B) can only be false if B is false and A is true. F -> F, F -> T, and T -> T all evaluate to be true statements. This seems a little counterintuitive, but if you substitute English phrases it becomes a little clearer. You can't really argue with "if Jess owns a unicorn, then Laura is a skilled contortionist," because I don't own a unicorn -- sure, Laura's not a skilled contortionist, but that doesn't mean that if I own a unicorn she's not one. We don't know, because I don't own a unicorn! Likewise, "if Jess owns a unicorn, then Laura lives in Seattle" is true, because Laura would live in Seattle whether I owned a unicorn or not -- at least until she moves to Chicago, at which point the statement will still be true. The only thing that would be false is "if Jess has funny-colored hair, then Laura is a skilled contortionist." I do, and she isn't, so that's wrong.
What does that mean for the hyper-digested form of the Vatican position? "If God exists, then evolution is true." Well, evolution is true -- anyone with even a rudimentary understanding of science knows this. Thus, for this position to be true, it's logically unnecessary to speculate on whether or not God exists. If God exists, we have T -> T, which is true; if he doesn't, we have F -> T, which is also true. As long as we know the consequent is true (and all this requires is a cursory look at the overwhelming evidence), then we can feel however we like about the truth value of the antecedent. Voila: hard logical proof that faith and science need not be mutually exclusive.