What I read about solutions with baking soda or washing soda is that they are being used for removing rust from an object by elektrolysis. I think the polarity is different then.
I don't know if it works in the same way as the vinegar for removing lead from the barrel. If the added ingrediënt in the water is just to make it conductive it should, but the solutions seem to be different for different objectives. I don't know the physics/chemistry as to how and why different solutions are needed.