Boeing : flying at night : You do not have to : I do not know the full plan , so I might talk nonsense, but for instance if you plan your flight at the right time ( end June for the North emisphere ) and fly enough North and at certain high altitude, you actually would do it in near constant daylight .
watch the site :
http://www.solar-impulse.com/fr/projet.php
they say they intend to fly at night but do not mention of the route..
Anyway good luck to them , to even attempt such a dream is worth supporting ! and I would not mind trying the glider !...