I think it does have a connection. My periods were like a clock every 28 days most of my life and about a year ago they went on totally weird timing. I even thought I had early menopause. Then slowly I started getting digestive symptoms too. But very soon since I started gluten free I got a normal period and now had it twice -even with a white head pimple...
I am very new to gluten-free, so I keep it simple(and try to eat as little proccesed as possible foods) - steamed cauliflower and green beans, potatoe salad(I made with pickles and homemade dressing), and organic chicken leg.