Yes. These are usually called "temp tags" and you can definitely use them between states - even though the rules surrounding getting and using them differ between states, all states respect each others' temp tag laws to the extent that your tag will not get you pulled over or charged. It's actually an interesting loophole near the border of states with especially lax temp-tag laws. The main issue you'll have to consider is insurance.

I know that here in Colorado it's possible to get a temporary plate for a vehicle with expired registration (the reasoning being that the vehicle should be registered to drive it to emissions/inspection), so I'm assuming AZ functions similarly.