No, miniSpark won't supply the power to the laptop. Actually, that was our original concept and the device you see in our Demo Video was designed to do just that. The cost to build that device, however, was very significant. So we decided to focus on an initial product that is a bit simpler and cheaper to produce. In the future we may revisit the possibility of making a full-featured power device with all the bells and whistles (voltage/temp monitoring, etc ...)
You are correct that the laptop has to stay powered. But the beauty of using WOL over say a USB wake device is that you can completely shut down the PC. You are not in StandBy or Hibernate so the power consumption will be significantly reduced (less than 1 Watt). We have not run into any car battery draining issues in our tests to date.
You could also use a Power Supply unit that can monitor the state of the car battery and disconnect power if necessary.
Thanks for your interest. We look forward to launching our product for sale as soon as our final testing is complete.