There is a definite connection, but not for all women and a lot of things can effect it.
I was always ovulate on the new moon and AF on the full... if you watch a lot of women in the ONE thread are cycling together and its usually within just a few days of the moon cycle... we tend to get a lot of BFPs or AF showing up around both full and new.
As for effecting fertility thats a load of bull, IMHO. As long as you are ovulating with a fairly decent lp length it doesnt matter what phase of the moon its during.
Artist, photographer, stay-at-home-mom and Marine wife. Mom to 4; a boy and three little girls.