No, sorry. While you can day hike up that far without a permit, camping overnight there requires the same permit as those spending the night higher on the trail.
But... When you go in with your reservation to pick up your permit, be sure to ask whether there are any overnight permits left for that day. It is always likely that there are some no-shows or cancellations available, and they will give you an overnight permit so you can camp there.
People have said it is a very nice place to camp -- usually nobody else, and very quite and serene.
