Since specific impulse and exhaust velocity are directly related via $$I_{SP}=\frac{V_e}{g_0}$$ anything that increases the exhaust velocity necessarily increases the specific impulse.
The issue is: do you gain anything from it? That depends on what "gain" you're looking for.
Rocket engines of any type are momentum devices. The impulse imparted to the vehicle by a small bit of exhaust being expelled (call its mass $\Delta m$) is proportional to the momentum of that small bit, and that bit of momentum $\Delta p$ is given by $$\Delta p = \Delta m \times V_e$$ where $V_e$ is the exhaust velocity.
But to get to that $V_e$ the bit of exhaust must be given an amount of kinetic energy $E_k$ that is proportional to the square of its velocity: $$E_k = \Delta m \times \frac{{V_e}^2}{2}$$ When you factor in the rate at which you're expelling that exhaust, i.e. the propulsion system's mass flow rate $\dot{m}$, you get a required power (energy per time): $$P = \dot{m} \times \frac{{V_e}^2}{2}$$ In a chemical rocket engine the chemical reaction in the combustion chamber supplies that energy. But in an ion engine, or other type of electric propulsion engine, that energy must be supplied by an electric power source (we'll ignore the power required to ionize the propellant, though that's not negligible when designing the power supply), and therein lies the rub: the mass of an electric power supply (of a given type) increases with the power it must provide.
You can increase the specific impulse of an ion engine simply by increasing the voltage across its grids, though you might have to increase the separation between the grids to prevent arcing. If you maintain the same propellant mass flow rate, voila! the thrust increases, since $$F = \dot{m} \times V_e$$ where $F$ is the thrust. But now the power required from the electric power supply went up as ${V_e}^2$, so you added a non-trivial mass.
Whether you get a net increase in acceleration depends on the system scaling before uprating $V_e$. If the system mass before the upgrade was dominated by the sum of engine mass, tankage mass, gimbal mass, etc. (non-power-supply stuff), then the increase in power supply mass might not overwhelm the increase in thrust, and indeed you get an increase in acceleration. But if the power supply mass began as a large fraction of the system mass, the relative increase in the system mass as a result of the increase in the power supply mass might be larger than the relative increase in the thrust, and the acceleration you get actually decreases.
Back to what is meant by "gain".
Say you're trying to get a spacecraft's wet mass down to fit on a specific launch vehicle, so you're trying to minimize the propellant mass needed for this specific mission's well-defined and large $\Delta V$. Then you might put up with a decreased acceleration (and likely a longer trip time) to get the decrease in propellant mass from the increased $V_e$. But if trip time is important, then higher acceleration gets more priority. Optimizing electric propulsion systems is an exercise in balancing such factors. This includes such things as the choice of the power supply type: solar? nuclear? That specific trade can go various ways depending on such things as the heliocentric distances over which the system must operate. Mission design engineers must weigh all those factors. The optimum $I_{SP}$ is one of the parameters that comes out of such analyses. More is not always better!
I know, I know, there are many people who would see that last statement, widen their eyes, tilt their heads back a bit, point a shaking index finger at me, and exclaim, "BLASPHEMY!!!"
