  It has been suggested that the Galactic Center Gamma-Ray Excess (GCE) could
be produced by a large number of centrally-located millisecond pulsars. The
fact that no such pulsar population has been detected implies that these
sources must be very faint and very numerous. In this study, we use the
contents of Fermi's recently released Third Pulsar Catalog (3PC) to measure the
luminosity function of the millisecond pulsars in the Milky Way's Disk. We find
that this source population exhibits a luminosity function with a mean
gamma-ray luminosity of $\langle L_\gamma \rangle \sim 6 \times 10^{32}$ erg/s
(integrated above 0.1 GeV). If the GCE were generated by millisecond pulsars
with the same luminosity function, we find that $\sim$ 20 such sources from the
Inner Galaxy population should have already been detected by Fermi and included
in the 3PC. Given the lack of such observed sources, we exclude the hypothesis
that the GCE is generated by pulsars with the same luminosity function as those
in the Galactic Disk with a significance of $3.4\sigma$. We conclude that
either less than 39% of the GCE is generated by pulsars, or that the
millisecond pulsars in the Inner Galaxy are at least 5 times less luminous on
average than those found in the Galactic Disk.
