Not too long ago I owned a motorcycle from the 70s. I realized at one point that it was probably EMP-proof: no fuel injection, no fuel pump, certainly no OBD anything, and a (literal) kickstarter. The most complicated thing in the wiring harness was the key cylinder and the relay for the turn signals and headlights. I miss that bike sometimes.
The ignition coil will probably not survive an EMP event, so the bike will not run.
However, it should be pretty straight forward to wind a new ignition coil if you ever find yourself in a post-nuclear situation.