Alternatively one could ask:
Would gravity favor sound propagation towards the gravitational center if it did not affect the static density of the medium?
The answer to this could be relevant, e.g., to validate numerical simulations by assuring that all physical effects are captured by the simulation.
For visualization one could imagine the medium to be a solid with constant static density.
The question arose from my personal image of sound being a movement of the velocity of molecules. Since the molecules are affected by gravity, the movement of the velocity might be too.
I believe this question is not a duplicate of How does gravity affect sound waves? because the accepted answer therein focuses on the indirect effect through static density change.