As a seasoned buyer every time I see a area rug over another surface I automatically wonder what the seller is trying to hide, especially when I see a rug over a rug.
If it were me I'd put the rugs away and save them for the next house.

I think a buyer can tell if the carpet is new, so I'd put them down to protect it.

As a buyer i question why an area rug is over a wall-to-wall, but usually it is just a decorative touch to compliment the decor...

As a buyer I would question why a rug was put in over carpeting, especially new carpeting. Are they hiding something? etc.

If you are putting in brand new carpeting there is no reason to put rugs down. You want to show off the new carpeting, not hide it. Also, rugs tend to be personal in taste and the less personal the house is the better.