Can celiac cause neurological symptoms like ataxia?

Yes: Neurological complications of gluten enteropathy are rare but recognized. Cerebellar involvement is one of the recognized syndromic manifestations. A neurologist should be consulted. Strict dietary compliance doesn't prevent these complications although as noted they are rare.

Unlikely: While there are theoretically vitamin deficiencies that could present as ataxia (I.e. B12), typically there would be multiple other celiac manifestations first.