You didn't address this part of the parent comment:

> I imagine it'd pull in electrons from all around itself, but I don't know how the numbers come out.

I never thought of it before but it seems like that should work. "Space" is actually a neutral plasma, right, so it should be full of free electrons. Those should neutralize the ship before any significant charge builds up. It seems like you should be able to use space itself (or more accurately the interplanetary medium) as a massive ground plane to complete the circuit for the charged exhaust beam.