So Cal might be able to? If it could, it's amazing they haven't tried it already... However, it would be interesting to check into. The question is, where do you source the fish for a California pond and is it legal?
So FL does have blue tilapia and butterfly peacock bass. With the mild winters FL has had the last few years, the peacock bass have spread much further north than the fisheries biologists ever expected. It seems almost all bodies of waters in that part of FL are interconnected by canals, so the peacocks found their way north using them. From what I hear, they're as far north as Lake Okeechobee. All it will take is one harsh winter and the fun will be over though. When I visited my aunt in FL a couple springs ago, I caught several small peacock bass, 9" or so. Some other oddities as well, Mayan cichlids, midas cichlids and oscars. I was fishing Lake Ida near Delray Beach... Good fishing for BG, RES and lots of Florida gar as well.
Butterfly peacock are the most cold tolerant, there are several other species but they die at much warmer water temps...