In case of a cascading powerdown, as during the large blackouts, the nature of the off-site power doesn't count. I.e., simplified, shutting down one plant shuts down the next, that the third and so on.
Are other power plants (coal-, gas-fired) also designed in this way?
Their off-site electricity needs aren't as big. (I'll try to dig up some numbers when I get home.) *Lunatic*, n. One whose delusions are out of fashion.
The external electricity need is an essential security feature of these plants: external power runs the cooling system pumps, as fuel rods have to be cooled even after an emergency shutdown (=no own power available). The emergency diesel generators are meant to run the cooling system pumps (along with the emergency systems) in case of an external power-down, though they aren't well suited to keep the power plants running, and are often weak links (at least poor maintenance of emergency diesel generators in US plants is widespread). *Lunatic*, n. One whose delusions are out of fashion.