[AlexandrB]

I don't think it matters whether you "boil" the water or not, you still need to put in enough energy to cause a state transition in the water you're evaporating. I see some papers on using ultrasonics to increase the efficiency of energy transfer from a heating element[1], but I don't think the second law of thermodynamics allows for a free lunch here.

[1] https://www.sciencedirect.com/science/article/abs/pii/S13594...

Edit: If you're thinking of something like an ultrasonic humidifier, I don't think these actually evaporate the water[2]. The mist these produce would still contain salt if you tried to use them for desalination.

[2] https://en.wikipedia.org/wiki/Humidifier#Ultrasonic_humidifi...