I know a lady who used AV pots for her begonias and claimed they did great for her. I have 4 such pots but only put AVs in them. Anyway, they are worth a try?

As for growing begonias in AZ, that is something you will have to figure out with the dry air. I would go only go so far out on a limb and say you will probably come to the conclusion that is easier to grow begonias indoors where you can keep humidity higher than the outdoor air. I've visited AZ twice and know there is a huge difference between Phoenix and Flagstaff. At least in Phoenix I saw huge Saguaro cacti, agaves, and Pride of Barbados bushes growing without a hitch. Flagstaff looked so green in comparison.