Would this be possible without any problems, assuming the size was right, etc. I would imagine it would probably need some sort of truss rod adjustment, but I'd like to hear people's opinions before I go and **** things up.
You'd need to fix the nut or bridge, I guess. Other than that, can't think of why not.

Go for it. Experimenting is fun.
I did it. now I have a left handed Tele(holy crap, it feels better to play with the body upside down) and a right handed "V-2" Also, so much better feeling upside down.
You'll have to get a new nut, you might need to change the bridge, adjust the inotation(sp?), maybe get new control knobs because having a Top Hat knob dig into your wrist isn't that much fun when you're playing