The answer to this question is very similar to a previous question with regard to concerns about the spread of germs by receiving communion (See: Stump the Priest: Communion and Germs). It does come down to whether we really believe what we say we believe about the Eucharist.
We cannot use gluten free flour to make the bread that we use for Holy Communion, and a person should be communed with both the Body and the Blood of Christ. Reviewing comments from Orthodox people who suffer from this disease, the comments generally suggest that they receive communion normally, and have no problems as a result.
I had someone who raised this issue with me, and because they were concerned about it, I made a point of giving them only a small portion of the Body. But as time went on, they eventually said not to worry about it any more, and never reported having any issues as a result.
Update: Also of interest is the following scientific study that concludes that a daily gluten intake of less than 10 mg is unlikely to cause significant problems to those suffering from celiac disease, even in extreme cases:
Systematic review: tolerable amount of gluten for people with coeliac disease
