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The compression of a gas produces an increase in temperature and therefore greater kinetic energy of the particles due to the exchange of momentum between the piston wall. Is this transferred energy also capable of producing a sound wave?

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Yes, but it needs to be fast enough. A loudspeaker acts as a piston that compresses and rarefies the air next to it, producing sounds.

There is a limitation on how well the piston can create a coherent wave pattern based on its size: it is hard to make a wave with a wavelength longer than twice the size of the piston. And for slow enough movement the diffusion speed of gas molecules will overwhelm the piston speed, and equalize densities faster than the piston can change them.

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