I don't think it would be a problem. China and Japan are the world's leading producers, and that suggests they grow well in a variety of climates. From what I've read on the subject, the only danger you might have in Arizona are cold winter nights - they need to be kept as frost-free as possible. At that elevation, I suspect you may have to plant it in a sheltered spot.
Here are some helpful sites:
from Clemson University Cooperative Extension Service
from Fruttilandia (doesn't seem to be a commercial site)
from the Farms of Amador project, University of California Agriculture and Natural Resources