Nope. And it doesn't make much difference. Your battery will run down by the tiny amount needed to keep that green LED lit, is all. I don't know how long it would take for it to be a measurable difference because I haven't tested it. It just doesn't matter enough to get me curious.
My CCX came delivered with the green light on but the battery was still above 50% charge. It's a very slow drain on the battery but should not be a problem as long as you are aware of it and turn it off before it drains the battery.