Does a skimmer remove salt?

Agreed. The amount of salt removed is usually negligible (especially in the face of NaCl-adding compounds, like all 2 part solutions), unless you skim significantly wet. Some people will pull quite a bit of very light skimmate--on the order of gallons per day, in which case salt depletion, coupled with additions of fresh water, will result in a net drop in salinity (essentially doing a continuous water change). This is possible because the bubbles themselves are composed of seawater, since the various ions tend to stabilize the bubble surface area--because ions are so strongly attracted to the polar water molecule, they come along for the ride. Again, this is not usually significant for the vast majority of ions and molecules in solution (unless they are organic, chelated, complexed, etc.).