Can I feed enough spin up electrons to a black hole to affect its angular momentum?

I infer that you are asking whether spin angular momentum can accumulate to a macroscopically significant amount.

It is generally claimed that spin angular momentum does not have a classical counterpart. So maybe there is no connection with macroscopic angular momentum at all? In fact, there is a connection with macroscopic angular momentum, which is vividly demonstrated by an effect called the 'Einstein-De Haas effect'. I'll get to that in a second.

About the black hole in your thought experiment: my guess is that you added that element to the picture because nothing escapes a black hole. That is, the fact that the electrons enter a black hole ensures that it is a one way trip.

Check out this youtube video titled Einstein De Haas effect, uploaded by the University of Michigan Demo lab

The demo shows a torsion pendulum.
The amplitude of the swing is back and forth around a vertical axis. The amplitude of the swing increases because the swing is pumped. The current in the surrounding coil is reversed in resonance with the natural frequency of the torsion pendulum. The Einstein De Haas effect is very small, the resonance setup accumulates the effect to a significant amplitude.

The particular metal in the setup, presumably iron, has a significant population of electrons with a spin that can be reoriented by an external magnetic field. Every time the current is reversed the direction of the magnetic field is reversed, and the alignable electrons realign. But angular momentum cannot change, so the electrons must exchange angular momentum with external mass.

I find the Einstein De Haas effect fascinating: you get to see a quantum effect accumulate to a level where you see a physical consequence with the unaided eye.

A single electron will already alter the angular momentum of a black hole by exactly $\hbar/2$.