Your equation is non-relativistic, and hence only works for small numbers.
What happens at relativistic speeds is that, from our point of view, an object will shrink in length, increase its mass, and time will run slower on it. As it approaches light speed, its length will approach zero, its mass will approach infinity, and time will approach stasis. You can find explanations in a lot of popular books on relativity.
In that equation, you're adding up a lot of little adjustments. A charge potential of 10^24 volts is effectively two potentials of 5x10^23 volts put together. You can view it as going through 10^24 one-volt potentials. Each of these is adding a little momentum to the ion. At non-relativistic speeds, a change in speed is proportional to change in momentum, but that doesn't hold at relativistic speeds.
What happens is that, when the ion is going well below light-speed, adding a certain amount of momentum gives a fixed amount of speed, and the math is simpler if we solve for speed rather than momentum. You could take your equation and add a multiplier of q on both sides, and you'd have an equation for momentum, but anyone using the equation would cancel out the qs because they don't help mathematically.
However, the effective mass of the ion is always increasing with relative speed, and so a given shot of momentum will produce less and less additional speed as the ion gets faster. As the ion gets really close to light-speed, it will increase its momentum almost exclusively by increasing its mass and only a very little increase in speed.
This doesn't mean the equation you've used is useless, because you can use it to figure out the momentum of the ion as it leaves the ship, and by conservation of momentum you can tell how much it pushes the ship.