Autophagy seems to follow a diurnal, circadian rhythm and sleep fragmentation seems to disrupt Autophagy (at least in mice Article Circadian rhythm of autophagy proteins in hippocampus is blu...
). I would thus conclude that sleeping habits probably influence Autophagy in humans. I have yet to come across a study suggesting the opposite direction of influence.
Moreover, as day-time feeders, we evolved to experience typically low flows of nutrients from our GI system at night. As such, mTOR was much less likely to be stimulated during the evening. (Modern midnight pizzas reverse this, however). With mTOR -- the master growth-vs-autophagy regulator -- less stimulated at night, or particularly pre-dawn, autophagy was possible, asa active mTOR inhibits autophagy. Also, there seems to be a robust literature documenting the role of melatonin -- high during sleep -- and autophagy, independent of sleep status: