Worst I've recalled seeing in amateur boxing was the wire popping out of a few mounts and having to be reset(though I've no idea what that costs). One of my friends had braces when we trained kickboxing and he had no issues while wearing the braces specific mouth-guard(maybe shockdoc?) He was one of the youngest and therefore smallest in the group too. We went pretty hard when we sparred, but since we were all good friends we did tend to pull our punches more when striking the face, especially with kicks involved. So, as Liza just stated in three words what took me a paragraph, you should consult the instructor. You certainly won't be the first person with braces who started taking self defense classes.