I'm not a expert but plugged in it may fry the battery, there is no computer to hit so I would guess it could still run if you can get it started.
Unplugged I don't know if it would drain the battery or not.
Found this if it helps.
In addition to other effects, a nuclear weapon detonated in or above the earth’s atmosphere or alternatively an E-Bomb (see below) can create an electromagnetic pulse (EMP), a high-density electrical field. EMP acts like a stroke of lightning but is stronger, faster and briefer. EMP can seriously damage electronic devices connected to power sources or antennas. This include communication systems, computers, electrical appliances, and automobile or aircraft ignition systems. The damage could range from a minor interruption to actual burnout of components. Most electronic equipment within 1,000 miles of a high-altitude nuclear detonation could be affected. Battery powered radios with short antennas generally would not be affected.
Chad Falstad "Hawk"
2011 HD Ultra Classic "angel"
2001 Nomad 1500 Sold March 2012
2001 VN 750 "Sold June with 2008 with 21,000""Serinity"