Is diarrhea considered to be a symptom of gluten allergies?

Yes: Diarrhea can be a symptom of gluten-sensitive enteropathy (celiac disease), but this is not a true allergy. In celiac disease, gluten (which is a component of wheat protein) causes damage to the lining of the small intestine, resulting in diarrhea, flatulence, bloating, vitamin- and iron-deficiency, anemia, and other problems. Some celiac patients do not have diarrhea. A blood test can diagnose it.

It's Possible: It's surely a common complaint of the food allergic patient.