Never waste cut roses, ladies.

For the beauty of the rose? Yes.

but potatoes are more beautiful

But the better question is, can you reverse it to get more potatoes

Theoretically, this is a sound idea. A potato is a root with nutrients stored well for plants which is possibly well-accessible for roses in the way indicated. The stems are soaking up nutrients and will soon develop it's own roots. A similar thing works with bushes, why can it not work with roses?

Also, roses come from bushes to prove harmonywho's point