Gamma rays are an early danger from the fallout from a nuclear blast.
Bunkers have different grading in terms of blast resistance and most of the AT&T bunkers were engineered for something like 5, 10, 15, or 20 mile air burst strikes of certain warhead yield.
The AT&T bunkers are mostly far removed from population centers such that a direct nuclear strike would be a waste of a perfectly good nuke. In reality, a directly targeted conventional warhead or sabotage would be plenty effective in causing major service disruption so I think a lot of the realities for survivability would be aftermath repair capabilities.