I've never seen anything like that. I think starting the genset is a manual process (to an extent) for safety reasons. You worried about sound? Fuel savings? Mine doesn't have an insulated box and it's not loud at all with the hatch closed. I think it sips about a gal per hour....small price to pay for comfort
That being said, there are house gensets that automatically "kick" on in the event of a power outage so it may not be out of the question.