Are there any studies that demonstrates the efficacy of a gluten free diet for autoimmune diseases?

Not yet but...: If such studies have been done I am not aware of them, but there is evidence that many with autoimmune disease have gluten sensitivity and i would be extremely surprised if a gluten-free diet did not result in significant benefits for these patients. There are no studies showing it would not help. See http://huff.To/1fnjx1a ; http://www.Ncbi.Nlm.Nih.Gov/pmc/articles/pmc2111403/.

Celiac disease: Celiac disease is considered an autoimmune disease, and a gluten-free diet is the main way of treating it therapeutically: http://tinyurl.Com/k98d4v7 also the paleo diet (which is also gluten free) has been used with some benefit in a pilot study of secondary progressive multiple sclerosis (also an autoimmune disease): http://tinyurl.Com/khgpl9g.

No reason why: Gluten intolerance is considered an autoimmune disease affecting a small but significant number of individuals. If you are not gluten intolerance, avoiding it would make no difference on other diseases whether autoimmune or not. However you will likely be less inclined to gain weight since so many great desserts contain gluten. No evidence that gluten issue leads to other autoimmune disorders.