Scooter,
My name is Gabriel Paz and I am the Law Enforcement Program Manager out of the Tucson Regional Office for the Arizona Game and Fish Department.
In Arizona we are blessed with multiple overlapping seasons that allows for most hunters to hunt several species of game at the same time. As we all know our rules are constantly evolving to not only provide hunters with opportunities to hunt, but also to restrict individuals from cheating. The creation of the Archery only season that prohibited carring any firearms was to try and catch those unethical archery hunters who were out there trying to create shortcuts for themselves so that they could shoot an animal with a rifle and ultimately tag it with their archery tag. Back in 2006 the department begain allowing for archery only hunters to possess the non hunting handgun specifically to address the issues and dangers we were seeing along the Arizona-Mexico border.
For those of you that doubt that there are hunters who would do such a thing, here is a quick story from my rookies days as a wildlife manager. I saw this first hand in the Willcox area back in 1997 or 98 when an archery hunter got bored so he traded his bow for a rifle and began hunting coyotes. After calling in a heard of deer with his coyote call he had the opportunity to harvest his buck and he decided to do it with a rifle (his bow was already put away in the truck). An ethical hunter out that day immediately called the OGT hotline and we caught the hunter as he left the area. Of course he claimed to shoot the deer with his bow but the evidence from the 30-06 bullet outweighed his arguement and he ultimatley confessed. For this type of violation he was cited for taking "taking a mule deer by unlawful method" since a rifle is not a legal method of take during an archery only seaon. Ultimately the overt action of actually taking or shooting at the specific animal during the "archery only" season is the only way an officer could issue a citation for this violation.
Now for the answer to your question, unfortunately this is one of those grey areas that is best answered by ThomC's response in the post before mine (I love that joke and I use it all the time when training new wildife managers). If you were hunting during an archery only season and you decide to hunt small game, you can lawfully use that pistol on your hip or archery equipment to do so. Just the fact that you decide to fire a handgun (an absolute No No for any archery hunter!) shows me that your done archery hunting for at least a while as you pursue small game.
I hope I answered your question!
Officer Gabriel Paz, Law Enforcement Program Manager, Tucson
Arizona Game and Fish Department