Yes, celiac disease can cause reflux symptoms and gastroesophageal reflux disease (GERD), both in newly diagnosed people who haven't yet adopted a gluten-free diet, and in people who have followed the diet for months or years.
Gluten appears to be the culprit in both cases when the reflux is related to celiac disease.
Reflux symptoms diagnosed as GERD are common in celiac disease patients who have so-called "classic" gastrointestinal symptoms, such as diarrhea, weight loss and fatigue, although asymptomatic celiacs aren't immune.
In fact, one study found nearly one-third of classically symptomatic celiacs and 15% of asymptomatic celiacs also have GERD at the time of their diagnoses. The gluten-free diet cleared up the celiacs' reflux symptoms within about three months.
However, celiacs following a gluten-free diet also experience reflux symptoms, possibly because of hidden gluten in their diets. Another study looking at lingering clinical symptoms in celiacs long after diagnosis found that about 28% of them complained of reflux symptoms they hadn't had at diagnosis. All were following a gluten-free diet.
Although researchers haven't studied the issue, anecdotal evidence indicates that exposure to trace amounts of gluten -- far below the usual "gluten-free" standard of 20 parts per million -- may trigger reflux symptoms in susceptible people.
Of course, there are many potential causes for reflux symptoms that don't involve celiac disease. You might be suffering from gastritis, peptic ulcers, Barrett's esophagus, or a Helicobacter pylori infection, which can cause ulcers. If you experience new and worsening symptoms, you should see your doctor to rule those out.
Carroccio A. et al. Clinical symptoms in celiac patients on a gluten-free diet. Scandinavian Journal of Gastroenterology. 2008;43(11):1315-21.
Nachman F. et al. Gastroesophageal Reflux Symptoms in Patients With Celiac Disease and the Effects of a Gluten-Free Diet. Clinical Gastroenterology and Hepatology. 2010 Jun 30 [Epub ahead of print]