I know from long years going to a holistic practitioner that women who are more "pure" in their diets, don't bleed as much. Mind you, anorexic women don't bleed at ALL, this is a different issue. I have heard it put that the more menstrual bleeding you have(unless you have some condition that is disrupting your reproductive or hormonal system) the more you are "cleansing out" every month. So I would say that that is probably fine for being on the cleanse.
I know that when I make changes in my environment and God forBID if I go traveling..that my cycle sometimes starts early.