When it comes to vegetation, Fallout is more or less a "correct" game.
Initial burn would cause immense damage to plants (forest fires as a result etc.) radiation too, resulting in extinction of many plants, but many more resilient species would survive (I'm totally excluding GECK).
Grass and such have a relatively short life span and reproduce rather quickly, and would easily survive.
Many tree forms, too. It would take time, but green life would recover.
Only real, actual damage that could be cataclysmic for plants is if the war resulted in massive amounts of dust, ash etc. to come into the atmosphere, which would basically block out sun's light and that would result in the total abortion of photosynthesis which would result in...yeah.
In general, plants are more resilient than animals (humans included), and will survive. It would take them some time, but they would grow, and Fallout portrays this pretty well (it's still largely dependant on climate - i.e. deserts aren't lush, but there are lush places - Zion for example). Falllout/2/NV are set in and around places which aren't really Norwegian woods in present day, so I don't see what's the problem here.
War would have consequences on climate change, I guess, but still not enough to kill trees.
If the series continues in the given chronological order, I don't think it would be surprising to see big forests, green fields and similar. After all, this series isn't post-apocalyptic anymore...
EDIT: Only now do I see what a gravedig this is...howly shit.