[SOLVED] Can an inverter on a car charge the house battery?

You have around 10% inefficiency on the inverter and 15-20% on the converter. So around 25% of the power generated by the vehicle is wasted doing this.

As mentioned above, an alternator at idle generates very little power beyond what it takes to operate the vehicle.

It would be much faster and cheaper to get a 2000W inverter generator to do the job. The expense of a $500 Predator is a drop in the bucket compared to the wear and tear on your car.