I've painted oil paint over arcrylic pictures that have been varnished. It worked just fine and are looking good. I don't know what it will look like 50 years from now but I won't be around so I don't care and I seriously doubt any of my pictures will be around either.
If the "varnish" you mention is acrylic medium you should have no probs so long as its clean. You can hedge your bets a bit by lightly wiping the surface with alcohol to reduce the gloss and slightly soften the cured paint. Such would also clean. As with everything, test on a small area before committing the whole thing.