"Friendliness" is (the way I understand it) a constraint on the purposes and desired consequences of the AI's actions, not on what it is allowed to think. It would be able to think of non-Friendly actions, if only for the purposes of e.g. averting them when necessary.

As for Bayesianism, my guess is that even a Seed AI has to start somehow. There's no necessary constraint on it remaining Bayesian if it manages to figure out some even better theory of probability (or if it judges that a theory humans have developed is better). If an AI models itself performing better according to its criteria if it used some different theory, it will ideally self-modify to use that theory...