If the clocks get good-enough, then yes, They'll keep getting better. To do it with a pair of clocks, there's a long way to go, as they measure differences in

If the clocks get good-enough, then yes, They'll keep getting better. To do it with a pair of clocks, there's a long way to go, as they measure differences in depth in a gravitational potential. If you change your distance from Earth's center by a meter, your gravitational potential will change by 9.8 m^2/s^2. If somebody heavy (100 kg) and spherical (I'm a physicist) stands a meter away from you, your potential will change by 7 x 10^-9 m^2/s^2. In short, the clocks need to get ten million (they can see a 1 cm height change) times better to sense a nearby person. Clever trickery with an ensemble of clocks will make that easier, but not by 10^7. Not impossible, just hard. The fact that the time/frequency teams have encountered gravity, in particular through the gravitational potential, has just made their lives quite a bit harder. They now need to know a lot about the relative locations of other clocks and the mass distribution within the earth to make substantial strides forward. It's an incredible feat to have gotten to where they are, and a major challenge for the future.