Should my advisor know if I am auditing unrelated courses?
In this case, you should let your advisor know, because the time spent in the classroom is time not spent in the lab. Since he's paying you for your time, if you will be doing daytime activities that will take time away from research he has a right to know about it. On a different note, depending on how auditing works in your university, there may be costs associated with your auditing the course, and he (or his grant) would be covering these costs.

Generally speaking, the more communication between you and your advisor, the better.