No, you cant use a power converter for an extended period of time while the car is off anyway.... because the coverter is probably only 60% efficent(give or take, depending on how good it is) so it will suck up a lot of juice draining your battery.... however that probably doesnt apply to charging the laptop batter while the laptop is off, because thats a small load.
i said... either buy a good converter. or dont use your Laptop pluged into the car.. just use the Laptop running off its own battery power. But when the Laptop is Off, you can plug it in to charge its battery if you stay using that cheap PowerConverter.
Do you need to use your Laptop often when your in your car? or for only short periods of time?.... because a good more expensive power converter can properly handle the electric current when the car is On/Running.... But when the Car is OFF, then any converter(probably even cheap ones) will get fairly stable power because its only running off the card Battery with no interfearences.
If you only need to use your laptop acationally in your car, then you can do it with that cheap converter, when the card is OFF. Ingnoring the GPS factor for now, if you need the comp on most of the time for other reasons, then i would invest in a Good/More expensive PowerConverter if i were you.
..... if you travel a lot because of work... and if you work for a company.... and if its work you need to be dooing on your laptop wen your on the road... then its more then reasonable, and the company probably woulnd have a problem paying or providing you with a Proper/Good converter for your Car.
Iv never used GPS..... and i may be wrong, but this is just what common scense is telling me... they may provide there service similar like phone companies... so you may beable to find a GPS service provider that provides the GPS Display unit for free if you sign up for there service... that way you wont need to use your Laptop.