I don't think GPS navigation systems that receive the satellite signals emit any signals, themselves. They only need to detect the signals from the GPS satellites.
I expect that the emitted signal from GPS navigation systems isn't a result of intentional transmission, but rather is leakage from the local oscillator that is used to down-convert (heterodyne) the GPS signal to a frequency range where it can be processed.
This technique is what police radar detector detectors use in areas where radar detectors are illegal.
Given the highly-integrated nature and size of modern GPS receivers, I'm surprised that there is significant leakage at all. Moreover, I would expect any leakage to be largely directed upward as that is the direction the antenna(s) are facing.
The other factor is that the onboard computer controlling the drone is likely emitting its own spectrum of radio noise so I don't see why that isn't also an issue -- one that will be common to any navigation method.