This is not quite how GPS works. Because of relativity, there is a difference between local time and remote time for all GPS satellites relative to the drone.
Jamming nowadays does not work by simply throwing off random numbers. This is trivially defeated by gyroscope. It works by feeding time data that initially is exactly the same as the satellite, and slowly changes that as if it was in some other plausible direction, ultimately giving total control.
Against primitive forms of jamming, sure this might work. Against modern spoofing attacks, no there is no fix. Overall, what worked works and what doesn't work won't.
Relativity doesn't really factor into this issue; the core of the issue is false timing signals.
Any introduction of a false timing signal whose time offset from the true signal is greater than the local clock's uncertainty can be flagged as false. Higher-accuracy local clocks reduce the amount of error that can be introduced without detection.
CSACs don't solve the issue, but they do allow for detection of more spoofing signals, and they reduce the amount of error that any successful spoofing signal can introduce.
No, relativity absolutely does factor. The timing signal from the GPS satellites is warped by relativity as you move relative to them.
Without a source of location truth, you have no way of knowing if the change in the time signal is because of your movement relative to the GPS satellites, or because of spoofing.
As I said, the false GPS signal will start with a time offset of zero. They will then progressively offset the time signal of each satellite as if, for example, the GPS receiver was deviating slightly right, after which the drone will turn left.
Relativity matters in GNSS in general, but it doesn't really matter for the issue of spoof detection; relativistic effects would be solved for by both the attacker and receiver. There's no uncertainty in them.
Relativistic effects dictate that it is impossible to distinguish changes in relative time and changes in relative position.
Because of relativity you cannot use local time to estimate remote time, and hence you cannot use local time to make the difference between time spoofing and location changes.
Jamming nowadays does not work by simply throwing off random numbers. This is trivially defeated by gyroscope. It works by feeding time data that initially is exactly the same as the satellite, and slowly changes that as if it was in some other plausible direction, ultimately giving total control.
Against primitive forms of jamming, sure this might work. Against modern spoofing attacks, no there is no fix. Overall, what worked works and what doesn't work won't.