The actual evaporation rates can be tricky. Sometimes the salt crust formed on the sides of the container help wick liquid up, speeding evaporation. So you can get the somewhat paradoxical result that the saltier solution evaporates faster for a while.
Your basic idea that the salt 'holds onto' the water is right though. At some fixed temperature the water won't all evaporate, but will leave behind a little stuck to the salt. The more salt, the more water left. They should all end up with the same concentration of salt.
As for how the salt holds on to the water, your idea makes a lot of sense. The tendency of the positive parts of water (H) to stick to negative ions and negative parts (O) to stick to positive ions can contribute to this effect, mainly by making it possible for lots of salt to stay dissolved in water. However, the biggest contributor to the tendency of solutes to lower the vapor pressure of water is something else, shared by even neutral solutes. It's that as liquid volume changes, the room available for the solutes to move around in changes. The formal way to say that is that as the liquid evaporates the solute entropy goes down. Nature always heads toward a maximum net entropy condition, so this favors keeping the water liquid, other things being equal.
(published on 06/12/2009)