I guess I always applied realism to this statement when Pearlman narrated it. There's no doubt the detonation of hundreds of warheads IRL, even just in the US and China, would cause enough radioactive fallout to poison most of the world, which would be spread through wind erosion and dust...
I definitely think the "boogeyman" status of the Enclave is a proper send off of that faction, and maybe some former members might take their military knowledge and training and apply it to their own individual lives (mercenaries, caravans) or maybe even apply it in a Gunner-like...