Most likely a bad thing, given similar past examples. E.g. I've talked to atheists who won't touch Bostrom/Anthropic Bias because they associate "the anthropic principle" with theological fine-tuning arguments. And the general problem of audiences' first impression of Bayes being that it's just another clever way to argue for whatever you want to believe or want others to believe.

On the other hand, it would be interesting to have more debates between theists and atheists who are both familiar with Bayes and use it explicitly, if the atheist is good enough at noticing and explaining flawed uses of it, so audiences can become familiar with fallacious uses of it and see that it can be used wisely.