This is kind of tough to answer, mostly because I don't want to get sued ... It really depends on the degree of hypoglycemia and whether it is because of an underlying disease (does not have to be diabetes related) or just because thats the way you are. The best way to make this judgment, besides a doctors advice, is trial or observation.
Really, everyone "fasts" for some part of the day: sleep. During the 8 hours of sleep (your doing that right? haha) you don't eat anything and probably drink very little. So how do you feel in the mornings after you wake up? If you get the symptoms right away-sweating, dizziness, headache-then I might do a protein-sparing-fast instead. If you feel fine after that, then maybe try it out, preferably on a day when your not going to be doing anything potentially dangerous (driving), at-least until you get an idea of how you react.
Hope that helps.