like red blood cells, or other cells that have no mitochondria.

So, what you say is true - as blood glucose drops below a certain level, insulin drops, and glucagon mobilizes fat from fat cells.  But, even still, the body maintains a bare minimum level of glucose in the blood for those cells that require it, but it's something like 2 teaspoons total of sugar - not very much.

For the vast majority of people, I think you can only go so low in blood sugar (well into ketosis, by the way) before gluconeogenesis kicks in.  It kind of makes an upper and lower limit on hypoglycemia or ketosis I think.