Yes, but a better clock means more precise measurements, means we can locate smaller masses to higher precision.
Inversion is rarely unique, and it's not due to the precision with which the field is measured.
https://earthsciences.anu.edu.au/study/student-projects/nove...
https://inside.mines.edu/~rsnieder/snieder_trampert_00.pdf
Epilogue:
Linear inverse problem theory is an extremely powerful tool for solving inverse problems. Much of the information that we currently have on the Earth’s interior is based on linear inverse problems
Despite the success of linear inverse theory, one should be aware that for many practical problems our ability to solve inverse problems is largely confined to the estimation problem.That said, the gravity technique is one that actually gets used today. With better precision, it can be even more useful than it already is.
A practical constraint is mass density, which has maximum and minimum values. We can make a crude approximation that the planet's density is constant, evaluate the field on the surface from the planet's shape and compare it with measurement. This would be more useful, but still, it wouldn't tell us whether there is a combo of water reservoir and a large massive deposit below it.
Sure this isnt going to be a star trek scanner but for practical purposes theres a bunch of other techniques to constrain the results
But now that you know it is there, you can use other techniques, like seismic measurements, to nail that down.