As the parent of an eleven month old baby I'm going to dispute that a lack of sleep does anything but make you reliant on caffeine, and useless at doing anything that requires actual thought.
I have anecdotal evidence to suggest that there is something to this. It's not so much coming up with original ideas as to knocking something up fast. Your mental censor is far more inhibited when you're sleepy and you're too tired to multi task so in a weird way you're actually more focused when you're sleepy if you're a mild ADD type.