No, the multiple comparisons problem, like optional stopping, and other selection effects that alter error probabilities are a much greater problem in Bayesian statistics because they regard error probabilities and the sampling distributions on which they are based as irrelevant to inference, once the data are in hand. That is a consequence of the likelihood principle (which follows from inference by Bayes theorem). I find it interesting that this blog takes a great interest in human biases, but guess what methodology is relied upon to provide evidence of those biases? Frequentist methods.