The problem is that I imagine it really wouldn't be all that different. Most people who play tend to cluster underground during night, and come up during the day. This would be pretty much the same playstyle except reversed. The only difference is that they'd have to deal with mobs at night, but really that's just a rough start. It's insanely easy to be self-sustaining underground(you get enough saplings from one tree to create more than it cost to cut it down. So wood is easily gained. Food can be obtained via an underground wheat farm. A bit harder than a tree farm since they need sunlight, but not really by a huge margin). I think you might need to think a bit more critically about what else you can add to the gameplay that would add to the experience and make it different.

However, you are aware that when radiation is involved rain is actually very dangerous? Fallout and such Water becomes contaminated and evaporation picks up the contaminated water and when it rains it's pretty much raining radiation at much more dangerous levels than just ambient. A more fitting analogy would be vampires.