I actually do like this idea. I would keep the sleeping to 2-3 minutes probably (enough time for me to grab a drink or use the bathroom IRL lol), but I think it would add an interesting dynamic regarding trust and paranoia. It would take some work to really implement it in a fun way, but it's a good idea.
Yeah, this is exactly why I wouldn't want to have it on while I'm playing the game. I usually don't have any music playing, so I can hear Zeds/other players, but when I do it's low-key, atmospheric stuff.