While that did seem like a bit of a long shot idea (and frankly I would have been thinking "yeah, nice imagination" had that actually been his ending), I was none-the-less disappointed to get to a conclusion of "you're less effective when tired", something most of us worked out when we were infants without needing any scientific studies.
I've tried doing it for about a month, but I've found that there are more pain-free ways of getting more out of a day.
My interesting (and entirely sci-fi) idea was that if brain cells shut down when you're tired, we could live permanently tired - brain cells would take it in turns to shut down and recover, so you'd never be quite as awake as if you were sleeping each night, but you'd also never actually be asleep.
I can't find a source right now (haven't looked particularly hard though), but I read an article a year or so back about some people who either never sleep, or sleep very rarely (and by rarely I mean, awake for weeks on end) - I don't recall. I also can't remember whether it was known to be genetic, or just assumed to be genetic, but either way I'm pretty sure it wasn't a case of "anyone could do this if they ..."
I am pleasantly surprised, like I just had an uncommonly good glass of iced tea.