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I'm not sure what's the "odds of death" tipping point where the society/world devolves into something you no longer want to be part of. If the chances of dying without a bunker are 1 in 1000(0) it may help. If they're 1 in 10 most likely not.

So the bunker could help survive the initial strikes of a nuclear war, assuming your country can quickly retaliate and end it before substantial or permanent damage is caused. Then again in a country as big as the US the chances of a nuclear warhead penetrating the defenses and landing close enough to be a real and immediate danger are relatively low.

But if we're talking about prolonged nuclear war, anything that would really upend social order, or actually endanger the survival of the species (nuclear winter), such a bunker is just a fancy coffin. They will never get the chance to get out of it. If they do there will either be scorched earth waiting for them, or some sort of society that would see the protected elites as enemies and a cache of resources