Yes and no. Yes, it does provide DC power at a low current (maybe around 3-5A DC). This would trickle charge the batteries if there were no load on them. However, we run our fridge via the inverter when traveling which draws about 45 Amps DC. Thus, the batteries still draw down while we travel.
Our F350 does have the extra alternator and could provide a lot more power, but we'd need to run dedicated cabling for that. That is on the wish list. We just haven't gotten to it yet.