The variations due to changes in elevation are orders of magnitude larger than the variations you're relying on using for navigation. Distance from the center of the Earth is the primary signal you're measuring, for better or worse. It's not just relative vs absolute. You can probably assume the sub isn't changing depth rapidly and ocean currents are long wavelength, which would allow relative measurements to be somewhat feasible.
However, nothing about this requires a new quantum sensor. Ship-borne gravity anomaly measurements have been around for half a century. The previous methods are more than precise enough. In fact, they were done on submarines first before ships - it's easier to measure without waves.
What's triggering this now? Something doesn't add up... If it were purely based on using gravity anomaly along track measurements as a "fingerprint", it wouldn't need a new sensor. There's likely another mechanism they're using or they're using it for other reasons in addition to navigation.
