You'll definitely see other people on the trail. I was up there two weekends ago, and we ran into several groups of people via New Army Pass. I met a lot of people who were going up via Old Army Pass, too, so you won't be alone.
If my experience from a couple weekends ago isn't reassuring enough, you can see on recreation.gov that all the 36 reservable overnight permits have been taken for this weekend. This excludes the day hikers but should be further confirmation that you'll run into other peeps.
Wish I could join ya! Have a safe trip.
