Sadly, no. But they won't react the same way as the elephant foot of Chernobyl, but the water coolant must be pumped in, and that requires power from backup generators. They could supply their own power, but without the draw from other power stations going down, it'd go into a sort of "gray" state where it doesn't output power otherwise it'd melt the lines.
At least that's what all my research concluded. I might be wrong, but that's what I found.
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