If you could use chlorine to dissolve the gold on one side of the split cell, adding salt as needed, I would think if current and conditions were in certain limits the gold chloride would form, instead of generating chlorine gas (or limiting chlorine gas that would evolve), once you had gold in solution it could be precipitated out of solution, or possibly plated out of solution, the membrane or salt bridge could keep gold on one side of the cell.
For ore the problem of base metals and all of the other chemistry involved in the ore, would possibly cause havoc with the electrolyte, but for ore maybe you could use the chlorine cell to generate chlorine and use the gas to volatize gold from ore in a roasting furnace where the suspended red hot powdered ore >900 degrees C is falling through the flue gases with chlorine gases rising through this flue, the ore could also be pre-roasted with NaCl, to help pre-chlorinate the ore, of course capturing these volatile metal gases in a scrubber, here the sodium hydroxide generated in the cell may come into play, although building a furnace and maintaining it safely would be difficult, it would possibly be easier to just bubble chlorine gas into a crucible fixed with an ability to capture volatized metals (such as gold chlorides), and try to chlorinate the gold in the gold left in the crucible (crushing the melt when cooled to powder and dissolving the now water soluble gold and other metal chlorides.
Even simpler would be to concentrate the finely ground powdered ore, roast it and use the chlorine generator to bubble chlorine gas into a hot solution liquid leaching process.
For ore the problem of base metals and all of the other chemistry involved in the ore, would possibly cause havoc with the electrolyte, but for ore maybe you could use the chlorine cell to generate chlorine and use the gas to volatize gold from ore in a roasting furnace where the suspended red hot powdered ore >900 degrees C is falling through the flue gases with chlorine gases rising through this flue, the ore could also be pre-roasted with NaCl, to help pre-chlorinate the ore, of course capturing these volatile metal gases in a scrubber, here the sodium hydroxide generated in the cell may come into play, although building a furnace and maintaining it safely would be difficult, it would possibly be easier to just bubble chlorine gas into a crucible fixed with an ability to capture volatized metals (such as gold chlorides), and try to chlorinate the gold in the gold left in the crucible (crushing the melt when cooled to powder and dissolving the now water soluble gold and other metal chlorides.
Even simpler would be to concentrate the finely ground powdered ore, roast it and use the chlorine generator to bubble chlorine gas into a hot solution liquid leaching process.