I want to purchase a jute backing area rug, which has shag carpet on the front of the area rug. My question is, will the jute backing lay flat on top of the wall to wall carpet that is already there?

It is not advisable to put carpet over carpet. The lower carpet has a tendency to rot and nest all kinds of bugs.

If it was an Oriental rug will an unsealed back it would because it will let the lower carpet breathe.

Chuck