Possibly, but I would imagine that it would probably involve messing around with the code in a save file...which I don't know how to do and is probably risky at the very least.
Some things that are worth noting about the Apocalypse challenge is that the only complete rule set that I've ever seen was made for Sims 2. While I absolutely love the concept of it, I have many issues with it. The main one is that it has some of the most ridiculously inane requirements I've ever seen...this being one of them. The fact that you're living in a "desert" has absolutely no bearing on anything in the game.
I've seen a couple attempts at rewriting this challenge for Sims 3 (none of which were done by Pinstar, the original creator of this challenge), but I didn't really find any of them worth trying. I've tried to rewrite this one, myself, but I find it difficult to come up with a set of rules that isn't the size of the Encyclopedia Britiannica while sticking with the spirit of the original challenge. I have since given up on it.