But the series combination of potato cells won't have the same voltage, so it's a little bit like putting batteries with different voltages in parallel. I'm not sure what the practical impact is of having different voltage sources in parallel.
The impact is that the higher voltage stack will drive current into the lower voltage stack of potatoes. Nullifying most, but not all, the advantage of having parallel stacks. The conventional answer is to use a diode to combine them, but then you loose some voltage across the diode.
Using a Schottky Diode will result in a lower voltage drop than a normal silicon one. A normal diode will have a voltage drop between 0.6 to 1.7 volts, while a Schottky diode voltage drop is usually between 0.15 and 0.45 volts.