Well, the chemistry is certainly right, assuming you use zinc nails and copper pennies; that would certainly produce a small but measurable amount of electricity -- a direct current battery, in fact.
I hope you'll forgive me if I admit that I didn't test this one out in person, not being willing to cut the plug off my cell phone's charger and try to wire it up myself. If I ever get stuck on a desert island with nothing but pennies, nails, and oranges, I'll certainly give it a try. I bet it would take days to get to full bars, though.