It's unlikely, given that many of our close relatives have a menstrual cycle of a length other than 30 days. The University of Wisconsin says
The duration of the menstrual cycle
varies with species; about 29 days in
orang-utans, about 30 days in gorillas
and about 37 days in chimpanzees.
Incidentally, the duration of estrus
also varies in these species; about
4-6 days in female orang-utans, about
2-3 days in gorillas and about 10-14
days in chimpanzees. Both the
menstrual cycle and estrus vary in
duration somewhat among females of the
same species. The figures given here
are approximations or averages.
The cynomolgus monkey, meanwhile, has a menstrual cycle averaging at 29.4 days. Other animals are much further from a lunar cycle:
The corresponding estrus cycles of
some other mammals are 28 days for
opossums, 11 days for guinea pigs, 16
to 17 days for sheep, 20 to 22 days
for sows, 21 days for cows and mares,
24 to 26 days for macaque monkeys, 37
days for chimpanzees, and only 5 days
for rats and mice.
George O. Abell, quoted by Cecil Adams.