Josh, you can try it. wbtravis is talking about the walk-in sites which are right below the highest backpacker parking near the trail head, and above the overflow parking down the hill a bit. If you get there at 8 or near dark, you will need to look around with a flashlight to find a spot. It is likely you will find one.
But... the walk-in sites are technically for one night only. And you would get better altitude acclimatization if you stayed up at Horseshoe Meadows. You could move to the Portal in the morning to get a walk-in spot.
Let us know which way you go, and how it works out. Hope you have a good trip!
