AFAIK this isn't how it works; the GPS provides a reference so the skew of the crystal can be measured as it drifts.
The crystal provides a local reference with low phase-noise, and the long-time-constant disciplining provides reasonable holdover performance.
The original post said "might" but it seems that's exactly what cell sites use (GPSDOs).
The WWV and WWVB atomic clock radio stations have 1Hz reference frequencies that might be stable enough to be your 1PPS reference if you designed your GPSDO to accept an external 1PPS.