If the inverter is on, it will draw some power. How much is really dependent on the inverter itself.
right now im using an old toshiba satellite for my carpc. i have it bunjee corded under the back seat and i have extended the power button leads to the front of my explorer. what i want to know is if i keep it plugged into a 100 watt power inverter while the computer is hibernating when do you think my battery will be drained to where i could not start my car?