It's may be subjective, but i think you all answer to the wrong question. My issue is not if a ghost (seems more a polteigeist) could exist in real-life. I don't have that answer, but it is another debate. (if you ask my mom, she would be 100% certain that they exist) You are in a science fiction universe, with some bits of fantastic, and some clever fourth wall breaking elements. In this universe, it is ok to have ghosts, ghouls, brains in jars, real-life weapons, some intelligent talking animals, robots and computers still working after 200 years, pre-war food that you could still eat, mysterious strangers randomly helping you, aliens, and even cults based around radiation. Wheter this could happen in real-life is a bit irrelevant.
My questions would be : Does it make sense in context ? Is is contradicted by other facts in the same setting/universe ? Is it consistant with what has already happened, what was already explained to your character ? Would someone in the same situation would react like that ?
I am 100 % OK with a ghost ingame, as long as there is not something in the Fallout series that proves without a piece of doubt, that ghosts can't exist. On the other hand, i am less confortable with everyone in Reno celebrating your victory agains't the enclave, as they kept a low profile and i doubt anyone except Arroyo, Vault 13, the BOS and San Francisco are aware of their existence, at the moment you did it. Same doubts with Ethyl Wright managing to make everyone sober in New Reno, as the rest of the game made perfectly clear that she was unconvincing (no member in the union), naïve (no clues for Tully), and have a short temper, even with people that would help advertize her group (if you're a pornstar). [Fallout 3 is full of 100% human inconsistent behavior. (Lucy West, Sierra Petrovita, Moira Brown, Little Lamplight...)]
The ghost even make more sense that some of your explanations.
Don't use my name in vain, mutant!
Also, seeing as the Chosen One comes from a tribe with hokey-dokey grass/drugsmoking crazy looney-popes (in my opinion), I wouldn't be one bit surprised if he saw ghosts/spirits now and then. Those with some spiritual power of sorts can sense ghosts or other spirits (which is noted in the RP when you talk to the shaman of Umbra Tribe), while the "civilized" people tend to not see/notice such themselves (or try to make a profit by stories of haunted houses). As for her being killable/loony woman with Stealth Boy, I can't say I ever did try to put her to rest other than the regular way from doing her quests, so I wouldn't know.
Also this.