It's a thought provoking question. I don't think I have ever heard that someone with celiac disease should not take vitamin C.

Vitamin C can be rough on the stomach, though, so I suppose it follows that someone with celiac disease might be even more sensitive. Although by definition, celiac disease affects the small intestines... it can do damage throughout the body. Gluten sensitivity is also known to cause lymphocytic gastritis....and those with celiac disease often have trouble eating anything without distress until they have healed up some. I've heard that aloe vera juice can be helpful in healing, for example.

I'd imagine one should take vitamin C with food (?), and cut back back if they notice unpleasant symptoms...and try again after they have had 6-12 months to heal? I'd imagine some forms of vitamin C are easier to tolerate, too. I've heard of buffered C, for example.

I'm guessing here, really! My opinion here would be that it is ok to take unless not tolerated, but that would be an individual thing.

I haven't had a chance to look through these recently, but maybe you will find some more info among these links:
Nutritional Assessment for the Newly Diagnosed