I think that one could certainly make this work. But pre-existing Bayesian filters are almost solely specialized for spam, so there would quite a bit of manual training of priors to reliably distinguish expected from surprising log entries. And because it is probabilistic, there will be a finite chance of false negatives, i.e., interesting events that get reported as boring.

More generally, program-generated log entries have precise, repeatable formats that make them much easier to detect and parse than natural language emails. So creating a filter using regexps (and perhaps a little parsing) to chuck the boring bits of a log is easy enough and is probably less sysadmin effort than training a new Bayesian system.