Charging the engine battery

No. I use a small charger that will plug into the cigarette lighter socket, assuming it is live with the key off. It is just a trickle charger and will not bring the battery back if it is very low. It you need to charge a close to dead battery the best way is still a separate charger plugged into shore power and attached directly to the battery. The problem with charging both the coach and engine battery's from the same source is that you have two dissimilar battery's with different levels of charge, it really will not work well and may even damage one or both.
Wayne