Not sure that simply switching off the a/p would have that much effect... cars don't have A/Ps and plenty of people fall asleep driving...many years back, my nights flying the Bandit ( no a/p) were plagued by fatigue... I'm someone who can't sleep a minute when travelling as SLF... whatever the time/length of trip, I'm awake... put me in front of those instruments and I begin to be hypnotised by the glow of the lights... lack of sleep..
On one occasion returning to 'Saafend' at the end of a sleepless week of night freight we arrived in the London TMA with totally cr@ap wx.. vis to mins...turbulence, icing the lot.. remember thinking "I'm going to have to stay awake for this" as we closed on the localiser.. remember thinking it again just as a hand slapped me on the shoulder as the F/O realised I was asleep !
I say again.. every bit as dangerous as alcohol and not nearly getting enough attention...