Like 100% shut? I've seen them nose into glue and get a glob on them but never fully glue their mouth closed. Heck, if that happened to one of mine I would wait it out for a day or two, keeping an eye on it to see if it resolves. At the same time I'd be looking for a fish trap just in case. If it doesn't resolve on it's own, do your best to trap it and get the glue off using super glue debonder, carefully.