Looking at the schematic for the SE2-A it seems to have all the necessary wires for the pickup (replacing the blend pot in your case), the volume pot, the battery clip and the output jack connected together via the preamp circuit board itself. The piezo ground doesn't get connected to the volume pot, it gets connected to the preamp. This suggests that if there was a spare grounding wire already soldered to the back of the volume pot (and not connected to the preamp circuit board via the dedicated connector) then this would be intended to be a bridge ground wire, as you indicated earlier - I think this could be removed rather than being connected to the output jack ground.
As for trying to ground the strings when you have a wooden bridge, I've read that some people have an arrangement where they have a metal retaining rod threaded through the string ball ends which then gets fed via a grounding wire to the output jack - though some have argued this isn't needed.