No it isn't. There is a clue in the question - fall. You'd have to be propped up against a tree or something otherwise you'd slither to the ground. It is possible to fall asleep if you are supported by something, a bed is a good idea.
My sister used to fall asleep standing up when she worked in a hotel - usually when she was on reception. She also sometimes slept with her eyes open, but I don't think she ever managed to sleep both standing up and with her eyes open, but she was always a bit dopey anyway, so I am not sure if we would have noticed!
its ok leewayne, they used to be someone else and hold a grudge just because I told them not to be so rude to someone else. Doesnt bother me really, just lets other people see what they are like :-) and yes fluff why were you tied to a tree, Drunken night maybe