Good question! I think you do in performance classes. I know youth count towards it. So why not ammy?? I know my gelding started in jumping 3 years ago has over 30 points from nothing. And I show open and ammy. So he has to becuase he wouldn't get that many points otherwise.
Is this for AMHA or AMHR? Ammy classes that do not lead up to Championship classes do not count according to page 328 of the 2008 AMHR Rulebook.
It is also noted that for example - Hunter class, where there is no Championship classes - on page 327 it is noted that if a horse/pony gains 70 points, special provisions exist for performance categories and upon the recommendation of the National Office a horse can achieve HOF status.