No, they don’t. They turn water into tiny droplets, which are then ejected from the machine’s port into the room (you can see this fog coming out of the machine). The droplets then rely on the heat of the room to turn them into vapor.
If you want liquid water to evaporate, that phase transition takes a lot of energy. This is why evaporative cooling (e.g. sweating and “swamp coolers”) works so darn well. Here are things that will work in your favor:
[ul][li]You can give things a head start by pre-heating your vessel of liquid water to somewhere close to the boiling point. [/li]
[li]You can go even further by working in a very hot, dry environment (think Death Valley, Phoenix, or Las Vegas). [/li]
[li]Atomize your liquid water as finely as you can manage. Liquid water evaporates at free surfaces; transforming your cup/pot of water into a collection of tiny droplets maximizes the surface area. Not only that, but smaller droplets have a lower terminal velocity, which means they’ll take longer to fall back to earth, providing more “hang time” during which to evaporate.[/li]
[li]Disperse your liquid water droplets into as large a volume of atmosphere as you can manage. This gives it access to a lot of atmospheric heat, giving the best chance of vaporizing all of that water. If you don’t do this, a little bit of your water vapor will saturate a small volume of air to 100% relative humidity, preventing the rest of the liquid water from evaporating.[/ul][/li]
According to this psychrometic chart (PDF), at 70F and 100% relative humidity, the air contains 110 grains of water per pound of air. IOW, for every gram of water you want to evaporate, you’ll need about 64 grams of air Got an 8-ounce (250-gram) cup of water? You’ll need to disperse that cup of water into 16,000 grams of air (this assumes the air was at 0% humidity in the first place). That’s about 13 cubic meters of air - a box 2.4 meters on a side. If you can atomize your water into adequately small droplets (as an ultrasonic humidifier does), then this will work.
The problem is that for a human flinging water by hand out of a little red Solo cup, the droplet size is going to be huge. Like raindrops. I can’t imagine any quantity of water that could be human-tossed that would evaporate completely before hitting the ground.