I would carpet the whole room, then put the riser in and carpet it.
If you ever want to reconfigure the room or change the layout of the riser or room, you're going to have a hole in the flooring, and good luck trying to match it after the fact.
You'll still need to isolate the riser frame from the floor. That reduces the "savings" on less carpet.
If you're going to be running electric or wiring or lighting in/under/through/on the riser, it's easier to service or change something if you can lift the riser to get to it.