I just successfully used this proposed setup to power my fridge during a power outage due to Hurricane Sandy. I purchased a Xantrex pure sine wave inverter, 1000W continuous, 2000W surge, along with a pair of #2 AWG 18" leads. I connected the negative terminal of the Xantrex inverter to an empty hole on the chassis of the car's DC-DC converter, as recommended on this thread. I used an extension cord to connect the fridge in the kitchen to the inverter in the garage, 25 feet away.
My fridge is rated at 6.5A max, and draws close to this level of current when it is first plugged in. However the typical draw is around 1A or less, with a total power usage of 2 kWh over 24 hours. So this target usage is well below the rating of the inverter and the DC-DC converter.
The day before the storm, I had charged the car to a full 12 bars. During the power outage, I used this setup to power my fridge for 8 hours, drawing 0.49 kWh total. The car dash showed 12 bars (full) and an estimated range of 100 miles when starting this setup, and after 8 hours was down to 11 bars and an estimated range of 90 miles.