The GC will add berries to the bush, often faster than the farmers can forage them.
However, as the number of berries on the bush grows, each
basket that they collect gets bigger and bigger, so it'll only take a few farmers to keep up with the GC's production. When the game is shut off, the GC doesn't produce more berries, so the farmers catch up.
To really see how many it can hold (and it may be infinite), you'll need to have as few farmers as possible (check their preferred job to be parenting, that seems to keep them distracted.
) and keep the game window open and running.
Or perhaps someone with a game that only has the GC left can keep theirs open and see how many berries he'll produce.