Hi Borek,
Yes, please see the attached drawing and see if this makes any sense. The battery and plates create an electric field that produces an ion gradient as shown with cations collecting near the negatively charged plate and anions near the positively charged plate. If you then stuck electrodes in the solution as shown, would the charge distribution cause electrons to leave the anions, travel through a load and reduce the cations without any redox participation from the electrode material?
thanks