No, i don't think there is as limit within the game engine itself.
On Hard / Milky mode, I kept it playing after completing , just to see how high her production would go. It seems to be based on a percentage of her current production, so it scales really high over time. After 11 digits (!) or so, it wraps the number to a second line.... and eventually a third line.
I forget exactly how much... I kept expecting it to throw a mathematical exception of some sort (integer overflow), but got tried of waiting. :D
Anything past 2,500 or so and she basically refills from zero to max instantly; nothing effectively changes after that.... but it was funny to watch XD