AMHR does not check teeth. AMHA checks teeth on mares and stallions only, BUT IMO a good judge should check on any horse, yeah I know thats not going to happen, but I would hate for a horse that had an bad bite place over mine in a halter class. Just because it has good conformation on the outside, doesn't mean it does on the inside. An overbite to me is a bad conformation fault. However also you need to know how this bite happened, whether its genetic, or an accident.
My filly has an underbite. Both parents have great bites. Got Gary Fleur too look at her and said it can be 10% passed on. Not huge, but still would have liked him to say 0% lol. Right now, she isn't for sell. Even though I had several people say they would like to buy her, but they won't take her until they realize she has an underbite. Thats just good business. Nothing yet has been done with her teeth. Will get it fixed though. Would like it to see it come back on its own, but I really doubt that.
My filly next year, still has the bad bite, won't be showing in halter but will in performance and color classes. If she still has the bad bite she won't be bred, but used as a good performance horse, just like anyother gelding only a mare.