Are there psychological symptoms of celiac disease that also go away with a gluten-free diet?

Probably: No one has looked at this scientifically, as it's very difficult to measures states of mind. However, it makes sense scientifically, as immune responses going on in the body slow down the mind and make one feel generally ill. Anecdotally, i've seen folks with real celiac disease feel better overall soon after successful gluten elimination, but it won't help those without the real disease.