No, Arizona does not allow you to hold an active real estate salesperson license if you are not an Arizona resident. You can begin the process of earning your AZ salesperson license while you are not a state resident, but when you apply for your license, you will need to submit proof of residency.
You can find all of the Arizona code and statutes regarding real estate licensing and the real estate industry under Title 32 Section 20 of the Arizona state code. The Arizona Department of Real Estate (ADRE) also has many resources regarding licensing.