It's a pretty well known fact that trolls can regenerate lost body parts, provided it wasn't removed by fire or acid, but can a troll really survive having it's head cut off? I know the rules say any body part, but i think having your brain separated from you and hoping to survive is just pushing your luck. Obviously hydra's and so forth can survive, as they have multiple heads and brains ready to back things up, but a troll normally only has one head.
Yes, a troll can survive that.
From the Monster Manual page 291
If the monster loses an arm, a leg, or even its head, those dismembered parts can sometimes act with a life of their own. A troll can even reattach severed body parts, untroubled by its momentary disability. Only acid and fire can arrest the regenerative properties of a troll's flesh.
It is clearly mentionned that the troll is untroubled by this momentary disability, so it won't die unless, like you wrote, it is killed with fire or acid.