I just played through the whole thing and I never once encountered a "ghost" so I'm pretty sure its fine without it.
He appears in the pools in set locations. There is one at the bottom of the pool, he flickers in the middle of the room with the underwater walkway, he "chases" you during the locker section, and you can see him after you climb the statue in the mall bit if you go look back into the hallway before you leave.