This is a great question!
To first order charging doesn't matter. What matters is the exit velocity of the ions, determined by the acceleration potential difference $V_b$.
In a simple situation the thrust is the velocity of the ions with respect to the spacecraft times the mass flow rate $dm/dt$ of the ions, and that velocity is determined by (something like) the acceleration potential difference between the plasma or the first grid, and the final acceleration grid.
In the simple situation it's not related to the potential of the spacecraft relative to other things, so the speed of the exiting ions and therefore their momentum won't be affected by the charge of the spacecraft.
However nothing is simple, and yes there can be a small coulomb interaction between the sparse ion plume behind the spacecraft and the spacecraft's residual charge, but that is usually not a problem because the electrons removed from the ions are also shot out the back with an electron gun which is usually aimed into the general direction of the plume. If the velocities are similar, then from a distance it will look roughly neutral and this effect will be minimized.
For more on that see
In your equation the m-dot or $dm/dt$ is expressed as the current times mass and some other things. The reason that it looks like the square root of mass is that the velocity term at the end $\sqrt{V_b}$ should have an M at the bottom which would then liberate the first M out of its square root and next to $I$ where it belongs.
For more on that see: