Of course, but much of the food for desert dwellers can still be grown in less drought-prone regions.

In the US, we have a fertile region in the midwest where there's enough water to grow millions of acres of corn just for ethanol fuel [0] (perhaps not sustainably given the state of underground aquifers, but that's another subject entirely.)

In drought-prone regions like California, we divert millions of acre-feet of water annually to grow especially thirsty crops like almonds [1] which aren't exactly a staple crop feeding cities. Current water policy is wildly unsustainable, but no politician wants to be the first to make an unpopular change in this game of drought chicken.

[0] https://biotechnologyforbiofuels.biomedcentral.com/articles/...

[1] http://www.slate.com/articles/technology/future_tense/2014/0...