Going outside of my area of expertise (in other words, speculating), I'd say no.
The adiabat is changed due to water evaporating as the temperature increases with pressure increases, thus reducing the temperature change. Heat transfer from air to water = not an adiabatic process.
With the pressure changes associated with sound waves propagating through the air, the water droplets will not have time to evaporate and condensate to any significant degree with the small pressure variations caused by the sound waves. In other words, (dry) adiabatic compression.
If the air had time to transfer heat to the water droplets, you would in fact be leaving the adiabatic process behind as heat transfer from the medium (air) into a reservoir (the water) would take place. As you point out, you'd be getting closer to the isothermal process assumed by Newton.
Makes sense? If not, I blame it on management!
Rgds,
/Fred