I don't believe there can be a false positive. Technically, there could certainly be a lab mistake, where your sample got mixed up with someone else's. The blood test looks for raised antibody levels- which simply wouldn't be there if you weren't Celiac.
Some Celiacs are "asymptomatic." They have no noticeable symptoms, but this does not mean that there is not damage being done to the intestine! Therefore, no Celiac would be asymptomatic forever. That damage will cause symptoms on its own eventually. (Intestinal damage = villi damage, which causes a myriad of problems: vitamin deficiencies, osteoporosis, dental problems, infertility, cancer...)
Also, it is possible to have symptoms that you are so used to, that you just don't really notice them. For example, upon going gluten-free, one might notice an increase in energy- when they didn't even realize they were feeling run-down. Or clearer, sharper thinking... or a cessation of "normal" occasional heartburn... migraine headaches that you may have attributed to something else... etc.
But even if you are completely symptom free-- if you are Celiac, then gluten is destroying your small intestine, whether you can see it or not.

Hope this helps.