@Johnshead,
The ions have to get their electrons from somewhere.
If you set the battery on the counter, and don't connect it to anything, the metal ends will have slight electrical charges, because the electrolyte mixture will have "pulled" some free electrons from one end, and "pushed" them to the other end.
When you place to batteries in contact, there will be a very tiny flow of electrons where the terminals touch, but not enough to really worry about.