They do, and my ride is licensed both on road and off road in AZ, plus we buy an AZ. State Lands permit every year. We stay longer, but basically you are good for 30 days on your home state license in AZ, but you still need the state lands permit.
We have friends in Cordes Junction, and have been in the country to the west of the 17, Black Canyon, Crown King. Checked out Roosevelt Lake while touring the Tonto Basin. We were just looking for timbered areas this year. What about around Show Low and south? Is that more Forest Service or BLM-State Lands?