Can sound be used for propulsion?

No, you can't. Here is why:

When a loudspeaker is producing sound, it is pushing forward to produce the compression part of the wave in air, then it pulls backwards to produce the rarefaction part of the wave, then forward, then back, etc. This means there is no net force applied to the air from the cone and no net reaction thrust applied by the air to the cone. Your vehicle would just vibrate back and forth as the cone works back and forth and no propulsion would result.

This is a difficult question, even for people who are physicists. I say this after reading:

https://www.physics.princeton.edu/~mcdonald/examples/hidden_sound.pdf

which discusses the concept of hidden momentum, a concept I've never heard of. Moreover, based on that article, it appears experts argue whether it does or does not exists in various circumstances.

The general idea is that sound waves move energy (density), $u$, at the speed of sound ($v$) in some direction, and that leads to an energy flux:

$$ \vec S = u\vec v $$

Following $E=mc^2$, we can turn that energy flux into a momentum:

$$ \vec p = \frac{\vec S}{c^2} = \frac{uv}{c^2} $$

which is tiny. It is in fact a relativistic effect, and is so tiny, that the author writes:

"It appears that the fluid-dynamics community generally considers that the laws of relativity are not relevant to this branch of physics, and that the momentum density can and should be ignored"

So the answer is "yes" if you're pedantic, and "no" if you are practical.