I remember one theory of why PCOS happens is exposure to androgens in the womb.
So it probably would have an effect on the brain, as we know it.
But there are so many people with PCOS who cry so much on how masculine and unfeminine they are and how deep their voice and people mistake them for guys on phones and maybe sometimes in real life too, that they kind of make the theory with relation to GID a bit inadequate.
Then again, it is also said about lack of androgen exposure in the womb causing the digit ratio (btw, most pcos women I know have masculine digit ratio, so another relation in favor I guess) be feminine in guys, this is also known to be able to predict * tendency* for gay sexual preference and GID, but still, most turn out gay rather than GID.
Perhaps it's related to the sensitivity in the brain, other chemical and genetic factors and the growing up environment in addition to the rest.