No, offense. But lets not bring reality into the Fallout universe. Because, first and formost. The half-life from the radioactive fallout from a nuclear war is going to last around 10k years. That's right. Around 10 thousand years. So, 200 years from the dropping of the first bomb I'd say anywhere from 50% to 90% of the planet will be instant death zones. Where the radiation would be so strong it would kill you in minutes. Now lets add into the fact that the Nuclear Winter would be lasting around a decade or so at least. So any crops or areas that didn't get hit are probably still going to mostly die off.
Here's a rather interesting and frightening article about what would happen if 2 countries with the smallest nuclear arsenals took each other out. How it would affect the rest of the planet.
http://www.popsci.com/article/science/computer-models-show-what-exactly-would-happen-earth-after-nuclear-war
Keep in mind this article is written showing about 1/10th maybe of the remaining nukes in the world being used.
Fallout itself is a game written around fantasy. Enjoy it for what it is.