Answer: I've searched for pampas grass on lists of invasive weeds in Arizona and cannot find it mentioned at all. It has become a problem in California so perhaps what you've heard is concern that it might become invasive, but hasn't yet made the official list. I know it is stll sold in nurseries all over Tucson and Phoenix. If it were on the official noxious weed list, reputable nurseries would not sell it. The problem with Pampas grass and other invasive plants is that they successfully outcompete native plants for light, soil moisture, and nutrients. As they increase in numbers, desirable native plant populations are reduced as are other plant, animal, and insect species that depend on the displaced native plants for survival. Pampas grass has caused serious resource impacts in Hawaii, California, New Zealand, and South Africa.
Wish I had more information for you. You might want to phone your local Cooperative Extension office for a copy of noxious weed list.
Best wishes with your landscape!
Q&A Library Searching Tips