Yes, that could be molecular mimicry. I hadn't heard of the thyroglobulin gluten similarity. But Hashimoto's thyroiditis is associated with celiac disease, which is clearly gluten related.
As the immune system matures in late fetal development, there's a stage when all cells that can target self antigens get killed. However, some tissues are isolated from the immune system, and so there are antigens there that don't get on the "self list". The thyroid is one of them.
Everything is OK until the thyroid gets damaged, infected or whatever. Then the immune system can see it, and may develop cell and antibody mediated responses.
Like all proteins in food, gluten is normally digested, and never makes it out of the gut intact. Only the component amino acids are transported to the bloodstream. However, in celiac disease, where the gut lining is damaged, I can imagine that some gluten gets across intact. Also many other proteins and complex carbohydrates.
Then the immune system could respond to all that stuff. And some of it could share epitope with thyroid components. So if there is an association between gluten and Hashimoto's thyroiditis, it's hard to say whether gluten shares epitopes with thyroid stuff, or whether it's just damaging the gut.