I remember being astonished when driving around the west end of Molokai and seeing that someone had planted a saguaro cactus on a desolate hillside. It must have been happy there, because it was about 10 feet tall. Now I have one that I am growing; in the past 3 years it has doubled in size from tennis ball sized to softball sized, and is starting to grow upward.
Saguaros, because of their very slow growth and propagation rate, are probably never going to be an invasive species.