Great question. Osmosis will be minimal when the total concentration of solutes in the potato’s cells matches the total concentration of solutes outside of the potato’s cells.

The problem here is twofold. First, the solute concentration in the potato is quite high as it’s low moisture and is comprised of starches, sugars, minerals, and other cell contents, so you need a ton of salt in the water to match the total concentration. Second, even if the solute concentrations are equal, making your boiling water an isotonic solution, you still have to deal with simple diffusion. The cooking process is blowing up cell walls, so some starch is going to migrate out while salt moves in to take its place. By mass, you don’t need to add much salt to a potato to make it unpalatable. You’d probably be alright with a whole potato but cut up potato pieces would end up really salty.