Rick, I have no reason to believe that there's any issue with running the engine while plugged in. Perhaps you are suffering from fear of the unknown? Can you point to a single owner's manual that say not to do this? That said, the only "connection" of note is at the battery, the shore power charger and the alternator connection, and this is no different than leaving your solar panels connected when you're plugged in - they just don't care. I am happy to learn something, though, if you can tell me why this is a problem, other than fear, uncertainty, and doubt.