Do you need to keep it powered even when the car is turned off? If you are using it only when the car is on then it won't be a problem.
You might want to get a dc/dc converter and use it instead of an inverter because it would be more efficient.
You could always go over to the technical section at
www.cleanmpg.com and ask the guys there. They know a lot about how the electronics in the car work and how much current you can pull from them.