You should be good to go. I'm using a laptop in my setup also. You haven't mentioned how you were going to power on your laptop. For my laptop (an HP), I took it apart and soldered two wires to my power button. That is connected to a relay powered by my radio's remote turn on lead using the one-shot circuit here: Schematics/Pin Outs/Diagrams.
I originally set windows xp to hibernate my laptop after 1 minute. That did not work. Apparently your laptop must be idle for xp to hibernate automatically--if music is playing, the computer is not idle. So I wrote a program that runs in the system tray that monitors when the laptop is being run off batteries(this would be when your inverter is no longer on). After a period of time ( I set mine to 30 seconds) the computer hibernates--whether it's idle or not. If you want the program, I'll send it to you.
For the inverter, I would use a relay to turn it on with the car/radio.
btw, if anyone knows where to get automotive relays cheaper than Radio Shacks $6-7 let me know.