I don't know anything about EMPs, except that it is said that an EMP will knock out anything electronic that has electricity running thru it or power to it, at the time of the pulse. So yes the electronic regulator and ECU would be toasted.
But
a points distributor does not use the ECU, and
you may have noticed that a good working regulator is not required to make or keep a car running; it will start and run just fine with the thing unplugged. However, without the charging system working, the battery will eventually get low enough to either not start the car, or not keep it running. You can get around that by full-fielding the alternator with the engine running, from time to time, to maintain the battery at full or near full charge.
But if the EMP takes out the alternator (not likely IMO), then yur walking.
I'm still having a hard time believing that an EMP can exist, or that it can do large scale damage if it did. But then; I do believe in;
giants and monsters, talking donkeys, special delivery by whale, and dead men walking, so .................
