No, on a narrative point of view, it's certainly not post-apocalyptic at all.
Because the bomb is a plot device to invent a setting made of cowboys, robots, fancy monsters and new world orders.
In Fallout 3 instead, the bomb is the focus, the protagonist: it's all about the effects of the nukes and what they made of the world.
In New Vegas, it's just a background element..... much like how the background element of Mass Effect was how human discovered the mass effect theory, but no one would say that Mass Effect's plot is about the mass effect!
So if you say that New Vegas is post-apocalyptic, then Mass Effect is all about the imaginary mass effect.
I'm tired of FO1-FO2 [censored] who shout "yes it's so postapocalyptic" only because they fear that admitting the truth would in some mysterious way lessen the quality of New Vegas. Hey, if you like New Vegas so much, then try to understand what the game is about! it's about societies, and fanta-politics. It's NOT about post-nuclear settings.