That would make sense to me. Trigeminal neuralgia at least is caused by direct compression of the trigeminal nerve root, which certainly causes some degree of inflammation. Inflammation is probably a minor contributor though; demyelination seems to be the main cause of pain in that condition. NSAIDs can treat the pain and inflammation there. Anticonvulsants are more effective because they directly modulate the firing of those nerve fibers and prevent them from generating a pain signal in the first place.