Wouldn’t nuclear power plants simply automatically shut down with all the safety measures they have? Maybe not all of them but probably not enough to cause a global catastrophe.
I'm certain all the reactors will SCRAM (shut down the nuclear chain reaction), but then every large (i.e. all) power reactors need active cooling to remove the decay heat and prevent a core meltdown.
(This is what happened at Fukushima - even with all the staff on site, they couldn't cope with a station 'blackout' (no external power grid) event.)