Using solar panels, and the resulting electrical energy, could an electron gun provide a suitable level of renewable thrust, better than an Ion thruster? If it would even create thrust at all that is.
Incident light on the solar panels will impart a momentum: The momentum of a departing electron will be
$$p = m_e v$$
Ion thrusters use heavy ions (such as xenon ions which are 235,000 times as massive as electrons) to get a greater impulse. From this figure alone, one can see that the propulsion from electrons alone would be quite small.
Also, keep in mind that when an electron is ejected from the gun, it leaves the rest of the device with a positive charge, which will increase the ionization energy. Ion thrusters get around this by ejecting high-mass positive ions with small-mass negative ions to retain a constant overall charge.
I know that's not a definitive answer to your question, since you're asking whether over very long time scales, such a device could eventually overcome this limitation.
There is another aspect to this, that is the level of energy imparted to the electrons, and the quantum state they are in.There will come a time, when we have the ability to impart near relativistic velocities to particles, and to change the way they behave. Bunching electrons into large Bose Einstein condensates will enable the macro effects of like charges acting repulsively to be more efficient in creating packets of thrust. However, you still can't get around the fact that you are limited by the initial rest mass of the electron, which means that although you can get some thrust when at relativistic energies, it still requires vast amounts of power to get them there, the only advantage of this system is that light is everywhere, and your "fuel" source is virtually inexhaustible, albeit orders of magnitude less and less effective as you move away from strong sources of photons, ie, stars...the better solution is to utilize matter, either as particles or ions, with a wide range of usable feed stocks is the way to go.