Do Narcoleptics really fall asleep on their feet?

So I'm a big fan of the film 'Rat Race'. And in the film, Rowan Atkinson's character is claimed to be Narcoleptic because he falls asleep twice, not just while running, but while standing. While I am very confident in the notion that anyone falling asleep on their feet would just collapse and not remain standing, I would like to know if people with Narcolepsy really do fall asleep while standing, running, etc.