As an autoimmune disorder, is celiac disease also caused by a chronic viral infection? If so, in what percent of cases?

This is nearly 90% viral. Keep in mind that wheat and wheat-derived products containing gluten are of extraterrestrial origin to begin with and not part of a normal Earth environment. So a sensitivity to gluten can happen simply because you are not designed to be exposed to that substance. But, in the presence of a chronic virus smoldering at a low level in the body, the juxtaposition of what the body might see as a foreign material can ramp up an immune response that inappropriately attacks the self. That is why it is seen as "autoimmune," a kind of aberration without a known cause. So this perspective provides an explanation of how such things get going. Eliminating chronic viruses that cause these damaging immune responses needs to be a high priority to reclaim health and well-being for a large percentage of the population given the many maladies that result.