I'd imagine that natural talent/aptitude and additional training will still produce enough variation. The "average person" baseline may be much, much higher making the gap between an "average Joe" and a virtuoso considerably less, but the difference is still real.
Plus, no matter how well you can teach people the technique of playing the piano, for example, artistry is another matter entirely.
“Artistry” is just mechanics. It looks like it would be possible to program not just the techniques but the thought patterns that give rise to them as well. So not only could the average guy paint the Mona Lisa, he could be programmed to paint it exactly the way Da Vinci did.