Using a significantly large metallic sphere, could we draw out the electrons from the negative terminal of a battery?
Yes, this is possible, you have effectively described using a battery to charge a very weak capacitor, then discharging the capacitor.  The charge stored will be minimal (possibly immeasurable), pico-coulombs or less and the number of cycles to fully discharge then battery may be on the order of billions or trillions, but in theory the process described is possible (more properly: plausible).