Unfortunately, the answer is yes and no. Yes, a gluten free diet will usually heal the symptoms but it will not cure the underlying celiac disease.
The Minnesota Mayo Clinic conducted a study of 241 adults in 2010 and found that:
“…More than four out of five of those celiacs experienced what doctors call a “clinical response” to the diet—in other words, their celiac disease symptoms got better or disappeared entirely. But after two years, their biopsies showed that only about one-third had intestinal villi that had recovered fully. After five years, about two-thirds had fully recovered intestinal villi.
People who cheated on the diet were more likely to have persistent damage, but so were people who didn’t cheat but who had severe diarrhea and weight loss and/or total villous atrophy (in other words, worse-than-average symptoms and/or damage) at diagnosis…
Because gluten causes the ‘T cells’ to attack the villi in your intestines, not having gluten in your system will usually eliminate your celiac symptoms.
“…You may need to avoid milk and milk products for a while. Once you stop eating any gluten, the intestine will begin to heal. Then it should be okay to drink milk and eat milk products…
On the other hand, no; a gluten free diet will not cure celiac disease.
Fortunately the vast majority of the medical conditions caused by celiac disease are eliminated with a gluten free diet. Diarrhea, intestinal cramps, malnutrition and other ugly side effects of celiac disease just go away without gluten.