If you had 1000 small propellors you could accelerate upwards many times faster than with 4 large propellors.
What are the rotorcraft experiments with the most number of propellors ever?
This guy is actually flying with 76 rotors.
But I might argue that your "more rotors is faster" idea may be flawed, smaller propellers are less efficient (because the further from the center you are, the faster the blade is moving, if I'm not mistaken), so the trade may be fewer, more efficient, propellers for a larger number of less efficient ones.
As far as I have come across there was a guy who had mentioned of working with 36 motors on a multirotor.