Results from experiments with polyphasic sleep are (Stampi, 1992; as summarized in Pinel, Biopsychology):
- Test subjects needed two weeks or more to get used to a polyphasic sleep cycle.
- Once test subjects got used to their new sleeping pattern, they were happy with it and showed no deficits in performance tests.
- Leonardo da Vinci's rhythm of 15 minutes of sleep every four hours works well.
- Most test subjects slept too long, and were not refreshed, or too short, and were groggy for a few minutes after waking up ("sleep inertia").
- At first, sleep is mostly slow wave sleep, but after some time the normal relation between slow wave sleep and REM-sleep re-asserts itself.
Stampi, C. (Ed.) (1992). Evolution, chronobiology, and functions of polyphasic and ultrashort sleep. Boston: Birkhäuser.
What I don't know and what would interest me:
In a normal monophasic night sleeper, among other things melatonin is high at night, body temperature is low, and, as your question hints at, there is a long break with no food intake. A polyphasic sleeper would disrupt these "natural" (i.e. corresponding to the rhythm of day and night) physiological rhythms, because he probably wouldn't spend his nightly wakeful hours inactive and in darkness. I don't know, what (longterm) effects this might have.
Stampi's book is rather old now, and I'm sure there is more recent research. Maybe some of these open questions have been answered by now.