You don't need to worry about lighting the contraction/expansion from pressure and thermal differences alone is going to be interesting to see, put a battery in a low pressure chamber and see what happens to it. I'm also wondering how they are going to deal with the temperatures and other aspects that can affect the batteries.

Solar Impulse flew at 15,000ft, a subsonic or transonic jet would be flying at around 35,000ft, the pressure at those altitudes is about 22-23 kPa and the temperatures are around -55 to -60c, and if he's aiming for supersonic he'll have another issue which is the fact that the temperatures of the aircraft can reach several 100's degrees C from the forces of friction alone.