Look, I don't really want to play with the tedium of voltage, but if you wanted voltage from the air, you need only condense the most static of gases, [oxygen]. This is the best conductor, so, will be the best source of energy. If you were to observe that if you rub your hands together, you will generate static, and you can apply that shock to whatever you wish, you could also use the carbon in the air, to bond with the oxygen - hey you got 'soot.' Soot is 'gaseous oil,' for lack of a better terminology, and oil burns easily, so, from the air, your best bet is to go to China, and, 'rub that stuff together,' yes?
If you were to merely condense the soot, you will have a sort of water vapour cola effort going on. If you were to spark a room filled with soot, enough of it, you will get a fire, in the air. This is because the carbon is just in gas form, and, has lost mass. This means that the carbon it he air can become a source for the energy to be generated, of course. This means, as there is conductive gas in the air, there could be a power source, although a weak one, unless you 'compress' it. This could be done by, as the op says, air compression, and, that is because the compressed air could also be viewed as a canister of aerosol, where it generates more mass than it has outside.
Converting this to voltage or something would require a 'beacon' or receptor in the area of the compression, of course. As mass is condensed onto the receptor, the energy, as mass is stored energy, will collect into the 'conductive receptor.' This could be made easier, with, water vapour. This would take the static and bond it to the beacon, and, then the energy would collect into the receptor, of course.
But, this is explaining it for kids, if you will. Yes it will work, in my opinion, no doubt.