Having the vehicle plugged in the and driving will not work.
On the J1772 plug thier is a pin called Proximity Detection. This is used to detect if the plug is in the vehicle. The vehicle will not allow you to drive away with it still plugged in.
The three large pins are for power and ground connections. The two smaller pins are for serial communications and Proximity Detection.
But your idea of extending the range via generator is a good idea.
Some changes to the car would need to be done. A special charging port would have to be added to the rear of the vehicle. A trailer hitch would also need to be added. Car would be able to signal the generator to remotely start and stop. The on board charger is only rated for 6.6 KW or about 8.8 hp. This in not enoph power to drive the car at 65 MPH, but can easily more than double the cars driving range at 65 MPH. If the FFE was driven at a slower speeds this would extend out the range further.
So before going on a long trip you would simply stop by your local Ford dealership and pickup your range extending Generator. I could see that if it becomes popular that car rental companies could also rent them.