We have a very similar unit at the office and that takes 1350 watts of power.
That is a lot of power, its almost 13A at 110V which is too much for a Honda 1000 generator and with an inverter you are looking at 120+ amps (more with the inverter inefficiency considered) and even the biggest 8D batteries are not going to sustain that for any period of time long enough to cook.
In general electricity is terribly inefficient at making things hot, gas is so much better. In the confined space of a truck its going to be hard to beat a gas grill.
Rob