it isn't all that likely to lead to a conclusion there's a God as commonly conceived

The Bayesian translation of this is "I'm an atheist".

While I'm on the subject, is there any reason to think Omega is possible? Or is Omega simply a handy tool for thinking about philosophical problems?

Interesting. I'm not sure I know enough about Omega to say. But for one thing: I think it is probably impossible for Omega to predict it's own future mental states (there would be an infinite recursion). This will introduce uncertainty into its model of the universe.