Until the battery is drained. The 55amp alternator can only put out about 800watts of power at 14volts. You would need to upgrade to the 120amp Saab alternator to power a 1500watt inverter without draining the battery.

That 1050 Watt generator isn't even enough to power a single normal refrigerator. EDIT: Nevermind, I just measured my fridge with the Kill-A-Watt meter and it only draws 200watts at full power and 600watts surge. You should be able to hook up an 800watt inverter to your car to run the fridge every few hours and keep it cold.