Yes, but the point of sweeping seems to be to add energy to a traveling wave front. You can still amplify the wave by sweeping faster and bumping the power at the appropriate time, but you would gain fidelity because you're not limited to single square waves.

No, the amplification can only work at the speed of sound, neither faster nor slower. The paper analyzes how the wffect falls apart when you deviate from c.

What you possibly could do is to have multiple laser beams forming a sweeping comb pattern. Depending on dispersiom and other effects, you might be able to do some waveform shaping. But that is very elaborate for a loudspeaker.

That's like saying audio over radio waves can only be sent with spark gaps... you simulate this "sweeping comb" with a fast sweeping, and even faster modulating laser.