I have the fear that ghosts being able to haunt people will cause them to annoy off other players, and, like players already ignore lights flackering and chair moving, the y will also be ignoring the ghost manifestation, or even people metagaming like, manifesting inside Interrogations from a guy that murdered you and pointing on the interrogated person and stuff like that to show other people, and this would really piss of the interrogated and so on.
Even though some good Roleplayers in Science or other departments may have fun in creating a Department for Paranormal Activity, the whole majority would either find it annoying or just ignore it as stated before and this wouldn't be worth the weight to code that.
The basic idea is good, but I don't think that it is able to be implemented in our playerbase, because I feel like, people that don't want to get involved in something, shouldn't be forced too (well, unless in Antag rounds of course).