So the bottom line is that yes you can put an area rug over wall to wall carpet.
How to get rugs to lay flat on carpet.
This should flatten the areas out.
However for rugs that are nowhere near furniture in the center of a hallway or foyer for example the carpet to carpet non slip pad is your best option for preventing ripples in your area rug.
With the towel still covering the carpeted area hold down the iron and press.
Double sided tape could be used in place of the carpet tape.
Cut tape to fit each edge of the rug.
Take a wet towel and moisten the areas where the carpet is curling.
Lay a damp towel over the edges and iron them flat.
Then take an iron and set it to a medium heat.
Apply the tape to the edges of rug.
Apply carpet tape around the edges of the rug.
Many times this will allow the rug to lay smooth for a while.