...the mice will play!
I think the meaning of this expression is pretty clear, and people say this for any occasion when a person's absence might allow the others to relax or do things they might not do normally. For example, in my department, our supervisor is on vacation, and if my colleagues and I decided to sit around chatting, go out for long coffee breaks, and generally play instead of working, we could say, when the cat's away, the mice will play! Sometimes people shorten this expression to just when the cat's away, because everyone knows the rest of the sentence.
P.S. Don't worry, JP, we're working! Really!
Image from Vangobot Paintings and Artwork