So let's say someone stored a bit of their soul in another person, deliberately. Could that bit of soul take over the person and possess them?
We know Harry was an unintentional Horcrux with a bit of Voldemort's soul, but that it did not ever take over Harry. Neither Harry nor Voldemort were aware of that piece of soul. There was a connection between Harry and the powers that Voldemort had, and once Voldemort returned there was an even stronger connection into Voldemort's mind. Yet Voldemort did not know about piece of soul in Harry, even after he tried to possess him in OotP and failed.
But what if someone hid their soul in another person on purpose? What if that piece of soul was more aware? Could it take over the person, especially if the person let it? We know Ginny's diary possessed her at times, so it seems possible to me. Then there is the locket as well, which obviously influenced the people who wore it.
Really, I think anything is possible with magic, so what's necessary to make it believable as a reader? What am I not considering when it comes to possession?
I think it would be possible for the bit of soul to take over the person it inhabitied. Like you said, Ginny was posessed by the diary and the locket did stuff as well, so it is believable. With the bit of soul that was in Harry, I think that it didn't actually do anything because of the fact that Voldemort didn't know about it, and also that Harry would have been too strong willed, I think.
The other Horcruxes acted independantly from Voldemort; the diary was able to enchant Ginny when he was body-less in Albania, so that suggests to me that he doesn't need to actively control it or tell it to do things. However, the part attached to Harry's sould didn't do anything, which makes me think that Voldemort perhaps put more enchantments and spells on the Horcruxes he had created before to make them act this way. Perhpas an 'ordinary' Horcrux just lies there and puts up a bit of a fight when it senses somethings about to destroy it. If this is the case then perhaps the person who is making the Horcrux in your story can enchant it to act the same way as the diary and the locket, the person could make it posess this person.
If not, then I think it would have to be a certain type of person who would become posessed. I don't think a strong willed character would come under it's influence, just like Harry doesn't, but someone with a weaker personality, or someone that the maker knows how to manipulate, would. I think that's what you need to make believable in the story. The personalities of the host and the maker, and also the way the Horcrux comes to posess the person.
Hope this helps and good luck with your story.
There are times when Voldemort's piece of soul influences Harry (like when he loses his temper in OotP). It's not clear how completely Voldemort controlled Quirrel in PS/SS. But from those incidents, and Ginny's diary, obviously people can be possessed, or at least influenced. The Imperius Curse acts very similarly to possession, though the caster isn't actually occupying the victim's body.
The victim's willpower would probably play a role. Harry is said to be very strong-willed in GoF (when he resists Imperius), which may explain why Voldemort was never able to do more than aggravate an already-short temper. Ginny, on the other hand, was an eleven-year-old... much easier to control.
It's probably rare magic, or people would have been more worried about it during DH (when everyone was taking precautions against Polyjuiced Death Eaters). It's also likely classified as Dark Arts.
Just to add to previous points made, I believe that it not only matters how strong the will of the victim is, but also how strong the person the piece of the soul came from. Voldemort was a very powerful wizard, and neither Ginny or Quirrel could withstand any amount of pressure from his will. Harry possessed a hero's heart, mind, and soul and therefore could fight back and win.
It all depends on how you measure a man, I guess. More to the point, what is the moral of the story going to be? Because if the moral is anything to do with the power of love, then a hero's ability to remain in control while under mental seige would be incredibly important, but if the humanity of your hero is a key element, then perhaps allowing them to suffer the effects of this attack would prove they are just the same as everybody else physically and mentally, but it's their heart that sets them apart.
Wow, that was total rambled guff, but...maybe a tiny bit of it somewhere makes sense?
Sorry if it doesn't =S
A lot of it could also have to do with just how you envision possesion actually works. Do you need a way to connect with their soul on a very deep level, or are people just essential giant meat-puppets that can be controlled through soley mechanical means.
In the books, Voldemort is probably able to controll Harry because they share a small piece of the same soul, which make sense. But then something else I have though about is the very cartoonish version of Voodoo where all you need is a part of someone's body, and then you can use a doll to controll their every movement...like a giant meat-puppet.