Yes and no. Per AQHA:
"Horses 5-years-old and younger may be shown in a snaffle bit, hackamore, curb bit, half-breed or spade bit. Horses 6-years-old and older may only be shown in a curb bit, half-breed or spade bit. Any horse of any age shown in any novice youth or novice amateur class may be shown two handed with a snaffle bit." (AQHA Handbook, pg 135)
Read more: Tips & Answers, please! :D
And the poster right under that reminded me that by hackamore AQHA means a bosal with mecate. You can use a mechanical one in speed events though.
Saw your thread and my mind skipped right back to that thread from a few weeks ago. ;)