Yes! You are correct. Gluten Intolerance can cause a lot of problems with in the body and often goes undiagnosed for years.
We have Celiac in the family and several years ago I went GF as a preventative measure and found that I felt SO much better without gluten in my diet. My ezcema on my elbows cleared up and I have not seen it since!
As a dietitian who regularly works with celiac disease, I have to jump in here and say that anyone who suspects they may have celiac disease should definitely be tested for it prior to going on a gluten free diet. You cannot be accurately tested for celiac if you're already gluten free. You are right that celiac disease can be a cause of infertility or recurrent pregnancy losses. However, in my understanding, the infertility is not necessarily related to PCOS.
Also, gluten sensitivity and celiac disease are NOT the same thing. If you have celiac, it is important to avoid all gluten, so that the gluten is not damaging the intestinal lining and increasing risks of nutrient deficiencies as well as intestinal cancers. If it's gluten sensitivity, it's more an IBS related type of thing and you the gluten is not damaging per se, it's just making you feel bad, and so you may still be able to tolerate small amounts of gluten without any adverse effects.