Charging the engine battery

Maybe. Most RVs, of course, will do the opposite: charge the house battery while the vehicle is being driven. There is typically some kind of isolator to prevent the house load from drawing current from the chassis battery while parked. Fancy isolators certainly exist that will charge in either direction, using intelligent algorithms that "do the right thing" depending on the voltages on either side. You would really have to look to see if you have one. A simple voltage test may or may not reveal its presence, since you might look at a time when the rules call for isolation. AK is correct that the odds are against you. This feature is relatively uncommon. it is an easy upgrade, though.