People with reservations are sent in first, the others draw numbers out of a bucket to determine processing order. However, all the reservation holders have to use a single desk/clerk, so if you aren't first, you have to wait. I stood second in line waiting over 10 minutes for the one person in front of me to get his multi-night permit (he was traveling into Sequoia N.P. so multiple nights locations, etc etc.) Then they have to verbally go over all the regulations and restrictions. (Do I sound annoyed? Well, I am.) Why they can't put all that written info on a page that people can print out and sign ahead of time, and carry on their hike, I do not know.
I wanted to use the night-drop box for my trip from Horseshoe into Sequoia, but Seki rules are that the permit MUST be picked up in person. So no night drop, stand in line... listen to someone tell me what I COULD HAVE read in advance, bla bla bla. Not to mention the extra hour and a half driving down from Horseshoe Meadows and then back up. All for their precious face-to-face time.
...but I digress...
They give you the wag bags along with the permit. I think the canisters are available right there, too. So it all shouldn't take you more than 20 minutes.
You should have plenty of time to pack into Trail Camp.