Those following a paleo diet avoid gluten. Beer contains gluten. However, some people react more severely to gluten than others. Personally, I wouldn't use it. I don't have a severe reaction to gluten, but I don't want to risk the damage it can cause. There are plenty of other marinade options. But, ultimately you have to make the decision for yourself based on the symptoms you experience and your personal goals.
"Beer contains gluten, which comes from the grain from which it is brewed. Only a fraction of the gluten that the grain contains gets into the beer. The proportion depends on the kind of grain that is used. The use of barley results only in traces of gluten in the beer whilst wheat contributes considerably more. It also depends on the brewing process. Generally speaking: the clearer and blonder the beer is, the less gluten it may contain. Some people are allergic to gluten and have to follow a diet that minimises or excludes their gluten intake. Whether beer can be part of such a diet or not, is dependent on the extent of the allergy and the beer type consumed. In many cases lager beers pose no problem for people who have a gluten allergy. However, it is up to the individual to assess his or her sensitivity."
I would also think that marinating followed by grilling would leave little residual gluten, but it might still be a bad idea for a celiac. Only you can know your tolerance. If it was me (and it often is) - I wouldn't worry too much about it. My wife pre-cooks brats in beer before I grill them. They don't cause me any issues. YMMV.