Once it starts going negative, you can't attack with it. It just says "you cannot issue an attack or transfer of 0 armies." As far as I know, it behaves the same as a 0.
And to knyte, 3,000,000,000 is an estimate. I think it's probably a little closer to 2,500,000,000, or somewhere in between--the slider moves the numbers so fast, you can't tell. And then clicking one at a time would, of course, take centuries. So I'm honestly not sure--somewhere between 2.5 and 3 billion.