In theory, yes.
In real life there are too few watts of heat produced by 12 volt, so it almost never cycles. Output varies by the square of the voltage. My fridge draws 34 amps on 12 volts, and because the wire is too small to support that there is significant voltage drop.
The only time the 12 volt works well is when I'm already plugged into shore power--so why the heck would I bother using 12 volts when I can use 120?