Oh gosh, how have I not noticed any? I think they would've stood out like a sore thumb.

There's also that feral population of Quakers in New York. They make these birds so expensive, but they're so harmful to our environment, makes me wonder why we can't catch them, and use them as aviary breeder birds.
I would imagine Cockatiels could make it in AZ. They are designed for the desert-like climate in Australia, so I would imagine they could make it here in the desert. Then again, we have some big hawks, and I would imagine they would be very easy to spot.