Your car burns about 2 gallons of gasoline per hour, yet the alternator puts out only about 1000 watts. That's not enough to run much. This means that your battery would likely run dead, too. Then you're left with no electricity, no car, and no gasoline.
Why not buy a cheap 1000 watt generator. They cost about the same as an equivalent power inverter, and only burn a quart, or so per hour.
My 4L V6 Dakota burns ~.35gal/hr @ idle