In theory if a spirit possesses a humans body the spirit would become the main being controlling the actions and the human would then be more of the subconscious observer. The human would be more focused on fighting the entity I believe, but it would see what the spirit would see I think since the spirit is in a human vessel, the human would not be the spirit, the spirit is now the human if that makes any sense. Of course I also feel possessions are very rare so unless the person willingly let the spirit enter their body [say you're channeling a spirit] it's highly unlikely one would be possessed and if they were [as I mentioned] the human would be preoccupied with fighting the spirit, and if it was channeling and the human willingly let the spirit enter their body, the human would be in a relaxed state and probably wouldn't be trying to see other spirits.
Usually when a entity takes over a human body as in possession they goes into a state of relaxation and consciousness and usually another spirit such like a demon is not going to want to mess with other beings, and also like said above a demon is going to use that body a do its bindings,
So be careful and try a banishing spell or ritual to prevent s taking over