After what I've just skimmed there... yes.

Make sure you read all the rules/regs though, don't want to get caught with your pants down. Make sure an air rifle is an approved method of taking small game, make sure you're hunting in a legal area, make sure you've got your license, and you should be good to go.

This map is better, you can get closer to Phoenix if you want.

http://www.azgfd.gov/h_f/hunting_units_mesa.shtml

If you have any specific questions, don't hesitate to call your local game warden/conservation officer/whatever you guys call them there.

They will assist you.