I certainly think a link between autism and autoimmune illnesses is worth looking into. The thing about autoimmune illnesses is that they are poorly understood, which also applies to Celiac and IBS which are part of the same family of illnesses.
What I can say from personal experience is that everything gets worse when my vitamin D levels are low, and vitamin D and iron get low if I eat gluten. This is of course personal.
However, from a lot of reading about autoimmune illnesses, it seems that very little is known about their causes. Generally, a lot of these illnesses are poorly defined diagnostically - just like autism, in fact. There is a lot of symptom overlap, which leads me to thinking that some diagnoses are really aspects of the same illness, or that one diagnosis may cover several different problems that result in the same symptoms.
There is now some documentation that vitamin D protects against allergy and asthma. I was diagnosed with asthma, which turned out to be vitamin D deficiency, not true asthma. Also, there is evidence that vitamin D deficiency during pregnancy can help cause MS in the child.
This is perhaps not exactly what the OP was asking about, but I think just looking at a possible link between autism and thyroid problems is too specific. There is more to it than that.