Okay not solely, but if you're deficient...which most people are, you'd be more prone to gyno.

"
Dr.Brownstein states that iodine deficiency results in increased ovarian estrogen production, as well
as increased sensitivity of estrogen receptors in the breast.

Eskin provides evidence for an anti-estrogen effect of iodine.

Wright has reported that iodine can help maintain a healthy balance of the three estrogens by
increasing estriol while reducing estrone and estradiol."

http://iodineresearch.com/hormones.html