I would expect that to be a bad idea. If the coats are going on rapidly enough to chemically bond, there is no need for polishing, and you would probably cause chemical impurities with it, as well marring the surface badly. If the coats are going on and mechanically bonding, a smooth surface is not desired, as the next layer would not be able to have any tooth to join with.

Possibly it would work under the varnish, but I don't see any need for it. The varnish creates the mirror gloss and depth, without any need for a polished surface to lay over.