The term you will want to use in your Google search is "Bayesian cognitive science". It's a huge field. But the short answer is, yes, the people in that field do assume that the brain does something that can be modelled as keeping and updating a probability distribution according to Bayes' rule. Much of it is computational-level modelling, i.e. rather removed from questions of implementation in the brain. A quick Google search did, however, find some papers on how to implement Bayesian inference in neural networks - though not necessarily linked to the brain. I'm sure some people do the latter sort of thing as well, though.
That said, being a statistical or philosophical Bayesian does not require one to believe this cognitive science hypothesis. If Bayesian cognitive science were soundly disproven tomorrow, http://www.yudkowsky.net/rational/bayes/ would still stand in its entirety.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.