There is some evidence of a connection. See this article. But it is hard to sort out what it all means. The "Wheat Belly" syndrome, and more. Luckily, I've tested negative for thyroid problems, though my brother has not. In my endocrinologist's notes, I see "normal, no evidence of AITD," which is the AutoImmune Thyroid Disease.
Added Note: So far the treatment is not different from what my GP has been recommending. If I qualify, and if I go with the PCSK9 regime, it would be different. (I think I would have discussed and gone with the increase in Crestor. But the testing has increased the sense of urgency...)