It has been suggested that a population of unresolved millisecond pulsars (MSPs) could explain the observed Galactic Center Excess (GCE). However, it has been claimed that, based on the luminosity distribution of observed MSPs, many would already have been resolved. In this work, gamma-ray MSPs detected by the Fermi Large Area Telescope (Fermi-LAT) and the GCE data are used to constrain the luminosity function through the use of a Markov chain Monte Carlo (MCMC) algorithm. The results indicate that it is indeed possible that a population of unresolved MSPs with the same luminosity distribution as those observed are the source of the GCE and that it would require further improvements in sensitivity for these to be resolved.