Yes. The wire will rotate around the circumference of the battery until it's out of energy.This will cause the entire battery to rotate in the opposite direction, and then come to a stop again once the battery is dead. This is the same as any Reaction Wheel.https://en.wikipedia.org/wiki/Reaction_wheel
May I suggest soldering the wire to the two end magnets, this would make the parts more together. If the experiment still works, then fix the magnets to the battery. It will be interesting to see what happens then.