What it looks like when Datura grows in a non-arid climate...

[Uli]

I have seen Datura species, probably the same D. wrightii in flower in Anza Borrego national park. This is a dry desert setting but the plants were lush and big but I assume that they had access to underground temporary water as there was a small stream nearby disappearing in the soil. But they must be able to survive long periods of drought. To do so their roots must be quite large.

In my garden in Portugal they very much behave like a geophyte, appearing very fast in spring after a complete winter dormancy. They are clearly summer growers and don't switch to my Mediterranean winter rain and summer drought climate. They do well only with some summer water.
I never dug up an adult root but I think it must be quite substantial as plants that come up in the wrong places from seed are difficult to simply pull up even as youngsters once they reach a certain size. The youngsters have a big carrot like root with a tendency to branch so the adults will have a big clump underground. 

[Wylie]

In the Azores, Datura is one of those weeds in the fields. While cows won't eat them fresh, they get cut with the grasses and aged so they can be fed to the cows in the summer. I think its close cousin, Brugmansia, is more attractive.