Ultrasonic "steam" tends to aerosolize the total dissolved solids. Google "white dust" in regards to ultrasonic humidification. I suspect that this would not work for desalination.
Aside:
I have a home-built ultrasonic humidifier. If I run it with Boulder, CO tap water that is low in TDS, it only takes a day or so to have a PM2.5 >600 in my house. For this to work I had to install an RO filter in order to humidify with ultrasonic and not degrade air quality.
Ultrasonic humidifiers need to be run with distilled or equivalent purity water, yes. Not just for the lack of salts being aerosolized, but also because anything that may incidentally grow in the water also will be aerosolized. Distilled water helps minimize growth.
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.
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.
Aside:
I have a home-built ultrasonic humidifier. If I run it with Boulder, CO tap water that is low in TDS, it only takes a day or so to have a PM2.5 >600 in my house. For this to work I had to install an RO filter in order to humidify with ultrasonic and not degrade air quality.