(I play piano, I took CM test every year up to level 8)
You can definitely create piano covers that include the vocals notes and sound good. I think just the video cletus posted isn't the best example of it haha
A cover is just remaking whatever song with whatever instrument you want, and you're not exactly restricted to only playing the instrumentals of the original song, you can do whatever you want to make a cover. For example, all the My Heart Will Go On covers. If we're just playing the instrumentals of that song without mixing in the vocals, it wouldn't work as a standalone song... I mean, unless the intention of playing is just to play the support instrumentals, then that's fine too, but it would sound pretty repetitive LOL