Autopilot or not, I think that common sense needs to apply. First understand your limits with regard to the risk of falling asleep while driving a car, and respect those limits to avoid actually falling asleep. Not worth the risk. And yes, there were times when I pushed my limits more than was wise when I was younger.
That said, at its current stage of development autopilot is not good enough to use as a strategy for pushing the drowsiness limit. It still has bugs (off ramp confusion, braking too late approaching stopped vehicle at highway speeds, etc.) and even when it stops absent a response to a nag, being stopped with emergency flashers in an active traffic lane is not my idea of a safe place for a nap.
As to the OP's original question of whether AP makes drowsiness more or less likely, I think that it will vary a lot by individual, so I doubt that there is a simple answer applicable to everyone all the time.
