There IS a correlation between the two. PCOS is known to cause low milk supply in about 1/3 of women who are diagnosed with it. PCOS effect about 15% of women, so only about 5% of women have this problem with PCOS effecting their milk supply and therefor not a lot of research has been done on it. It is heartbreaking to think that these women have so much trouble just getting pregnant and carrying a baby to full term and now they have a 1 in 3 chance of struggling with milk production too, which can halt BF.
So what did I find. I found that PCOS is caused by hormone imbalances which can cause the following symptoms: an irregular or late onset of the menstrual cycle, fertility problems, recurrent miscarriages, excessive body or facial hair, head-hair loss, acne and weight problems, insulin resistance and blood lipid abnormalities. Gestational and adult-onset diabetes can also occur. PCOS is now seen as a potential marker for heart disease in women due to insulin issues. While PCOS symptoms usually start in adolescence, in some women they do not develop until their early to mid-twenties. While PCOS is treatable, and long term improvement is obtainable, there is no cure. (Information from mobimotherhood.org)
The reason why this causes low milk production is according to Lisa Marasco, (leading researcher on the correlation between PCOS and low milk supply) there are several different ways that PCOS could potentially interfere with breastfeeding. (the following information is from mobimotherhood.org)