I concur with what Machka stated about structuring your sleep around an REM cycle (90 minute increments), and also have found that 5 or 15 minute catnaps on the side of the road can do wonders for refreshing tired eyes. I've also found the following tricks can be useful for waking up on a bike (though, of course, these tricks become less effective as you become more tired)
- eat something light and sugar-y (ie. energy gel)
- if riding with others, maintain conversation.
- if riding alone do a recursive, but not completely repetitive mental exercise
* sing 99 bottles of beer in a foreign language,
* play I Spy with yourself and keep on looking for items in the landscape in sequential alphabetical order)
* if you know alternate numbering sequences, every 10 seconds, try to express the mileage to the next control in hexadecimal or binary.
- sprint, do intervals or add additional bits of stress to your body
I've used all of these in some combination to get myself to the next control and a hot cup of coffee or to the sunrise, where the natural illumination will help me stay awake. I can say though, for certain levels of fatigue it is certainly very possible for one to fall asleep while pedaling a bike. I've done it and I've seen others fall victim to it.
It might be that you'll never fall completely asleep on a bike, but you will nod off enough that you will veer in one direction or another. In some of these circumstances, your body will hit you with a titch of adrenaline when you're on the verge of losing your balance on the bike and, before you've completely lost control. However, if you're unlucky that point of waking might come right after you've swerved into the oncoming traffic lane and are about to be hit by a car; or right before you've veered into the path of another cyclist in your pace line or right before you hit a pothole that will fling you from your bike.
In all cases, if you do find yourself micronapping, the best solution is sleep. It's better to arrive a little late than to arrive in an ambulance.