Yes, you absolutely can have celiac disease without having diarrhea. In fact, you can have celiac with constipation as your major digestive symptom, you can have celiac with no digestive symptoms, or you can have the condition with no obvious signs or symptoms at all.
A decade or two ago, "common knowledge" held that almost everyone who was diagnosed with celiac had voluminous, smelly diarrhea coupled with abdominal pain, and was rail-thin due to weight loss caused by the condition. Since then, however, medical research has shown that it's only a minority of celiacs who have diarrhea, and many people are overweight, rather than underweight, at diagnosis.
In fact, there are more than 100 potential symptoms of celiac disease, and most of them don't involve your gastrointestinal tract at all.
For example, a recent study in Ireland found that 40% of people listed diarrhea as their main symptom. However, another 34% said they didn't have any digestive symptoms at all in fact, in more than one-fifth of those ultimately diagnosed, the primary symptom was anemia, which may cause only vague symptoms. Women with celiac disease were less likely to have gastrointestinal symptoms than men with the condition, although it's not clear why, according to the researchers.
Another study this one involving family members of celiacs who themselves were tested and determined to have celiac disease found so-called "classical" celiac disease, with diarrhea and weight loss, in only about 28% of all people who were diagnosed with celiac disease.
Meanwhile, a total of 45% of people in that study had "subclinical" celiac disease, meaning even though they had the characteristic intestinal damage found in celiacs, they didn't have classical celiac symptoms. Instead, many of them had autoimmune conditions that have been linked with celiac disease, including thyroid disorders and psoriasis. Others, meanwhile, had atypical celiac symptoms such as reflux.
Finally, another 28% of the people diagnosed with celiac in that study actually had silent celiac disease, meaning they had no obvious symptoms at all.
People who showed diarrhea and other classical celiac symptoms tended to be older than those who had subclinical symptoms or silent celiac disease, the researchers said.
Therefore, if you're wondering if you should be tested for celiac disease (perhaps you have family members with celiac, or you have other autoimmune conditions, such as type 1 diabetes, closely linked to celiac disease), you should talk to your doctor about testing even if you don't suffer from diarrhea it's quite possible to have celiac disease even if you don't have that symptom.
Tajuddin T. et al. Clinical presentation of adult coeliac disease. Irish Medical Journal. 2011 Jan:104(1):20-2.
Tursi A. et al. Prevalence of celiac disease and symptoms in relatives of patients with celiac disease. European Review for Medical and Pharmacological Sciences. 2010 Jun;14(6):567-72.