a battery creates potential difference by accumulating more electrons on the negative plate.
That's true in a sense, but for a battery how the electrons got there (pumped by electrochemical reactions) is probably more important.
Therefore the more electrons that accumulate on the negative plate, the higher the battery voltage.
Well, yes, but those electrons will only get there to the degree that the electrochemical reactions are working. Basically, a battery whose electrochemistry can pump the voltage up to 1.5V is going to stop at 1.5V -- it's not going to overshoot to 20V or something. And if you went and applied an external voltage to the thing (therefore forcing electrons onto the negative plate and taking them from the positive plate) then current will flow "backwards" in the battery, either charging it or damaging it, depending on what kind of cell it is.
"More electrons on the negative plate (vs. the positive plate)" is a valid way to describe voltage -- but it's really a much better mental model for a capacitor than a battery. In the case of a battery, it's probably better to model the thing as a pair of plates with a "magic electron pump" between them that tries to force the plates to maintain a certain voltage difference. That'll keep you going unless and until you want to dive into battery chemistry and learn what's really happening (which would be right there in a 2nd-year University chemistry course).