I am going to be contrary and say that it could be a workable idea, but I had better back that comment up otherwise Caprirs and Kipper are going to be all over me.
On many commercial machines the way covers do a very good job of keeping stuff away from the guides and ballscrews.
The abrasive material is going to be in a suspension or slurry not an airborne powder and the speed of the polishing head is going to be slow so it is not going to carried in an aerosol. Indeed I think most of the compound is going to remain on the work piece and it would be possible to have a tray with tall sides to catch any splash.
The polishing pocess itself would not require coolant but I would arrange coolant nozzles to copiously wash down the way covers so that any polishing compound that did escape the tray would be collected and carried in the coolant.
It would be necessary to have far better than normal filtration for the coolant circulation but this is feasible.
Really when you consider things most CNC machines actually circulate a very dilute polishing compound in the coolant in the form of aluminum oxide particles. Just about every coolant tank on a machine running aluminum has a sediment at the bottom of the tank that grades down from discrete chips to a grey sludge; this sludge is mostly aluminum/aluminum oxide particles.
Would I use one of my machines for this application? Yes, a few years ago I bought a Haas GR510 and one of the intended applications was to try and develop procedures for doing decorative sanding and polishing on sheets of stainless or aluminum. Often hand finished sheets are used as panelling inside such things as elevators; I figured it could be possible to do the same thing in a controlled manner to actually sand pictures. My idea was to greyscale the picture and assign different grit sizes to the grey levels. The whole project did not go anywhere for a variety of reasons but being worried about polishing on a CNC machine was not one of them.