Rob, the plating won't come off in the kind of setup used to remove surface crud . Bagsy has reported that a little chrome will come off where rust has already gotten under the surface, but you'd spot that kind of rust damage before putting a piece in the soup. I've used zinc plated wire as the conductor lead and it doesn't come off the leads attached to my cookware, only on the leads attached to the anodes. 'Course, I've only done a dozen or so pieces so far.
I understand that chrome can be electrolytically stripped. There's probably a plating service in or near the closest city to you. Calling them might be a good idea if you're concerned that the plating on your piece might be ruined.