Running xbox through cheap inverter will add lots and lots of noise into the car audio. You can buy expensive pure sinewave inverters for a few hundred dollars, but we are talking more than the xbox here.
If you are only using it for occasional game use, and not for xbox media centre, then the noise is bareable, just be sure to attach a wire between xbox ground and the car - before that it is unusable.
p.s. or convert a pc dc power supply to xbox (different voltages etc) and enjoy a quiet setup.