I don't think solvents would be the issue. I've seen similar sprayers, even used one once, they're made to be used with brake and carburetor cleaners, which are very hot solvents. some of the ingredients in those are the same as what's in plastic cements. I would be more inclined to think the problem with using paints in them would be a clogging issue from the solids that are in the paint.
Good point. Cleaning it may be a pain. Discharge, empty, add cleaner, blow through, discharge, etc.