If you can assume constant lighting it would seem pretty easy? ask the user to move out of frame, take an image, and that's your "green screen" - difference current input fromt the camera vs the reference image of the users room, and overlay whatever doesn't match (e.g. the user) against their choice of background.

This is an entirely naive approach with no research into the problem done, and I can see big problems (such as "assume constant lighting"), but it doesn't seem too complex at a distance. I'm sure there's a video editor out there somewhere fuming at my ignorance though.