I'm of the belief that a world war today, which immediately launched all existing weapons to cause as much damage as possible, probably wouldn't wipe out the human race.
As soon as you launch that many weapons, and kill such a high percentage of people, you eliminate the possibility of manufacturing new weapons, so the war would be instantly over.
And I believe that despite others simulations to the contrary, there will be small groups of people who will stay underground for years, surviving on tinned etc. food. After 5-10 years, radiation levels will still very high, but most dust will have settled, and the skies clear enough to start to grow crops and rebuild.
Humans, as well as many other creatures, will become more radiation hardened over generations, and given the bountiful supplies of tech and resources left over from our civilization, will be able to quickly repopulate the world.
