It would be so awesome if you could basically make the anode and cathode be the rebar. Then your construction method would be almost identical to a regular building, with some additional wiring.
I don’t know if lye is still active (if that’s the right word) after the concrete sets. And this article says concrete has a high pH that resists corrosion.
https://www.concreteconstruction.net/how-to/rebar-deterioration_o
both lye and concrete are acid and caustic but lye is not Portland cement.
Rebar is attacked by chemical processes as it ages inside reinforced concrete. That is why bridges are built with epoxy coated rebar. Some electrical charging is sometimes applied to bridge reinforcement to counteract ion transfer.
The cathode will erode and the anode with build up material. That would be unfortunate.