Hi. No, you cannot register it there without having an address.
Arizona is pretty high on the registration fees. They will also want tax if it was not previously registered in Az or California. I don't remember how much our 5'r was exactly. Think around $500 a year or so registration.
If you are there for the Winter, less than 6 months, and leave it in storage for the rest of the year, you are not breaking any Arizona laws, since you are not occupying it. Storage lots in Az are full of snowbird rigs that leave their coach there all year. 90 percent of those are registered in other States.
Most storage is VERY expensive there, and you would want covered storage, which goes for a premium. Depends what part of Az you are in also. In Phoenix, we paid 5500.00 a year for a 75' covered storage.
We have been Az residents since 1997.
