There is a lot of plant life in the Mojave Desert and in F:NV's Mojave Wasteland. Plants like Joshua Trees and Mesquite are well-adapted to the climate and can found all over the place. F:NV's communities do engage in farming out of necessity, but they do not typically get good yields because farming in the Mojave Desert can present a lot of problems.
In the real world, agriculture was common along the Colorado River among the Paiute tribes because of easy access to water, but the soil presents many issues. First, the soil in most of the desert is sandy and doesn't hold water well. Second, the soil is typically alkaline, which affects the ability of many crops to grow there. Finally, some of the Mojave has a layer of caliche (hardpan) running a few inches under the surface. Roots have a difficult time penetrating the caliche, which is why many desert plants have broad, shallow root systems. Farmers have to break up the caliche if they want non-native crops to take root.
All that said, people still do grow crops in the desert. It's a pain, but it can be done. Some people grow crops that are native to the environment and others just do the best they can by painstakingly dealing with the soil and water issues.
