I can't see how there would be any grounds for disciplinary action or most work places would be empty. Also the fact that the management haven't taken any action against him over numerous complaints suggests they don't give a damn and thus won't bother here.
As for this conversation - firstly I'd recommend she says I have no idea if it took place as it's presumably in the middle of a longer conversation and also ask, what the heck he's doing listening into alledged personal conversations when he's supposed to be working. Doesn't look good from his side.
Don't think you can classify a private conversation being overhead in the same light as say phone tapping (not covered by the RIP act for one thing), but if he's got any sense he won't try anything as there are too many questions to answer from his side. Plus if he causes problems for the management, they are much more likely to take note of reasons to get rid of him.
In a nutshell - talk about him as much as you like and as openly as you like, he might finally get the message!