I know that tesla's won't allow you to drive while charging the car. It throws an error if it's plugged in, so, that's a no-go without significant hackery.

That said, they certainly have tow-behind generators, and they're certainly available for rent, it's just without modification you'd have to stop in order to charge. I've seen people with a model X doing exactly this out in the desert. Seemed to be an ok solution honestly, because they were camping and had genset power for camping needs, assuming of course that the whole electricity while camping thing is something you're into.