Well I don't know jack about Arizona laws, and it never crossed my mind to look them up. Many states will accept a different state's license as a valid driver's license. Do you have one from where you are? According to the state laws, not municipal, you don't need a license, now that could be different depending where you are, check local laws too, they sometimes place restrictions.
Here's the kicker, if you operate it faster than 20mph,then you need to have it registered licensed insured and ect as a moped, now that would very much be dependent on being caught driving more than 20mph,if you are it looks like they would impound the bike, and fine you.
So look at driving under 20mph untill you've become familiar with how the law is applied and handled by the police. Talk to other people with motorized bikes when you arrive, ask them how the cops are about motorized bicycles around there, and even better, follow up with the local pd, ask them how they feel about the subject, look for a sergeant to talk to, if they generally have the 'it doesn't bother me at all but I have to say you can't drive faster than 20mph but if you do I wouldn't feel as if I had to pull you over' kind of attitude then you should be fine as long as you keep the speed limit for normal traffic and don't interfere or heed normal traffic flow.
Research, I know a lot of members here are from Arizona, see if you an get the opinion of a person who live near where you are planning on moving.
Good luck, have fun, wear a damn helmet.