|MadSci Network: Astronomy|
An electric discharge, by definition, is when you have two objects with different charges, and electrons pass from one to the other, "dis"-charging the objects (with respect to each other). For example, lightning is an electric discharge between a charged cloud and the neutral earth.
If you were to have a discharge from a spaceship, you would need something to have a discharge to. In principle it is possible to charge up a spaceship and discharge to the surrounding space plasma (space isn't empty, but is filled with a small amount of charged particles called a plasma), but it wouldn't gain you much. A bunch of electrons would go flying off your ship, and your ship would move a tiny bit in the other direction. But electrons are very light and the discharge probably wouldn't have enough momentum to do much, in terms of propulsion.
Heavy ions, on the other hand, are charged particles that weigh much more than electrons. If a spaceship was able to throw out a spray of heavy ions in one direction, the ship would move in the other direction.
This sort of ion propulsion system is actually on a NASA spaceship which will fly by an asteroid this July. The spaceship is called Deep Space 1, and (after a false start) it has successfully shown that this type of engine can propel a spaceship. So yes, a sort of "electric discharge" -- firing ions into space -- can move a ship. Of course, electrons have to be fired off as well to keep the spaceship neutral, or there really would be a discharge when it got near the asteroid in July!
There is another way to use electricity to move around in space, and that is with an electromagnetic tether. These tethers are basically long wires that stretch away from a spaceship. If you put current in the wire, and if there is a large magnetic field nearby, you can "push" off of the field and move your spaceship very efficiently. Several successful tether experiments have flown already. Of course, this technique would only work around Earth, or some other planet with a large magnetic field.
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