Turn over the rug with the right side down.
How to get rugs to lay flat on carpet.
Double sided tape could be used in place of the carpet tape.
Take a wet towel and moisten the areas where the carpet is curling.
If the ends still curl up move to the next steps.
Apply carpet tape around the edges of the rug.
Cut tape to fit each edge of the rug.
With the towel still covering the carpeted area hold down the iron and press.
Then take an iron and set it to a medium heat.
Apply the tape to the edges of rug.
So the bottom line is that yes you can put an area rug over wall to wall carpet.
Many times this will allow the rug to lay smooth for a while.
Turn over the rug and lay it on the carpet.