Using a raspberry pi as a GPS NTP timeserver greatly amuses me since the raspberry pi doesn't ship with an RTC (or at least last time I checked). As a follow up question, how does the system time get set on one of these time servers? Does the NTP process have rights to update local system time or does the system rely on requesting NTP from itself?

System time gets set either from the GPS signal if not connected to the network or another NTP server if you are at boot. The satellite gives you a coarse time directly (accurate to milliseconds I think), plus a high precision frequency reference driven by the onboard atomic clock, which NTP uses to keep time. Once setup, this thing is supposedly capable of stability in the microsecond range, which is better than you'd get relying on an external server (dunno if true yet however).

NTP can set your system time I believe.

Lack of a RTC doesn't matter in this case because you wouldn't want one, they typically aren't stable enough. You're not supposed to turn it off very often anyway. If you were more serious about it than me you'd probably add a rubidium oscillator to serve as a secondary reference when GPS is offline and hook the whole thing up to a large battery, so that it never turns off. I don't care that much though, I'm just having fun with cheap toys.

Interesting, I’m doing the same but using WWVB 60khz radio signal for my time source

Also cool. I opted for GPS because I had a spare Pi and you can get dubious but perfectly adequate GPS modules for $3 off of Aliexpress, it's kind of an impulse buy. I also picked up a MAX7219-based LED display for another $2, so it's also going to be an over-engineered desk clock for $15 + some 3D printed parts (the other $10 is for a Pi Zero W I had left over from a different project).