It's unlikely that any damage will occur ... and extremely unlikely that anything but the power supply is at risk anyway.
I've used many MSW inverters to run many laptops and have never had a problem.
But, in my mind, the best thing to do is to see if you can get a 12v power supply that will charge the laptop directly.
I purchased just such a unit for my Acer netbook for less than $8 (including shipping). The one for my Acer laptop was also bloody cheap at $21 (the laptop one is higher current and will work with either my netbook or my laptop ... the notebook one can charge my laptop's battery but doesn't put out enough power to run it).
http://www.ebay.com.au/itm/250831081552So much easier to hook up (one end in the cig. lighter, the other in the laptop).
Bonus is that such a solution is more efficient too (not important when the engine is running, but when you're counting the AHs every bit of waste hurts).