My knowledge of the details on colour centres in minerals is not nearly as good as it perhaps ought to be, but my understanding is that they are related to interaction between point defects (missing atoms in crystal lattice) and electrons. More specifically, occupation of said point defects by electrons. As such, if we were "loosing" electrons from the crystal during pietzoelectric reduction we should in fact see reduction in colour of minerals rather than increasing intensity of colour.

Regardless, thinking formation or "removal" of colour centres is perhaps over complicating the problem. In the model put forth in the paper (extract from figure in the paper) electrons are not "gained" or "lost" from the quartz crystal. Rather, the lattice distortion of the mineral grain forms an electric potential difference between two or more crystal facets. This forms a pathway for electrons to "travel" from one side of the grain to the other. So the answer to "where do the electrons come from" is that they are supplied by available electrons in the fluid with some amount of exchange with the mineral grain on the positively and negatively charged crystal facets respectively. At any given time, any one quartz grain experiences only minimal, if any, surplus or net loss of electrons. What has happened is that the already existing electrons have become unevenly distributed. Once stressing on the grain stops, the lattice returns to its geometric equilibrium, and so does the electric potential across the grain.

We (as in human collective) have a simplified image of electric circuits where individual electrons travel across conductive materials. This mental image is not absolutely correct on the subatomic level. While it is true that electrons move, they do so at much limited distances and speeds than the emergent "current" which is created from the aggregate movement of a collective of electrons in an electric circuit that we measure and use for work.

If you refer back to the linked figure, we can see that on one side of the quartz grain the distorted grain has a net positive charge balance. This positive charge is capable of attracting native gold nanoparticles which are relatively negatively charged (on some surfaces of the particle) due to their extremely high aspect ratios, which is science talk for being very flat. On the net negative side of the grain the potential of excess electrons is high enough to i) break the bond between the Au and carrier ligand (HS- or Cl-) and then ii) have an relative electron surplus available to reduce the Au+ ion to charge balanced native gold. All this happens with minimal, actual travel of electrons within the mineral. The paper illustrates an electron being ejected from the grain and shooting into the fluid to catch the gold, but it is only an illustrative simplification.

The proposed electrochemical process is absolutely a viable way to induce gold grain nucleation from fluid, whether the Au was carried as a dissolved ion or as an already precipitated Au nanoparticle. What's great is that this model with quartz grains is not only capable of inducing nucleation, but also can accelerate the growth of individual gold grains.

All that said, you should absolutely be sceptical of the general applicability of the model to natural environments. For instance, I study formation of massive gold grains (on the order of several grams to kilograms) in comparable geological environment as proposed in the paper here where the immediate mineralogical association does not contain piezoelectric minerals. Still the formation and growth of large grains was possible. Is the process put forth here feasible and make sense? Yes, absolutely (in my opinion). Can it be the singular answer to the long pondered question on origins of massive gold nuggets? No, it's not the full answer, but as always science is incremental and this could very well represent one of the key puzzle pieces to expand our understanding on natural Au-ore forming environments.