Apparently, yes. LAX is a "Choice Service" location which imitates the Emerald Aisle concept from National. If you're a regular customer, you line up to receive your contract but aren't actually assigned a vehicle at the counter, but rather get to choose from a section in your reserved class. If you're a Bluechip, you will have a car assigned to you in the lot, and if you want something else you then take the mirror hangtag from that car and go pick something else from the row of cars in your reserved class.

I've never done it, just reading from the blurb on their website, and as far as what cars to expect I wouldn't be able to weigh in on recent experience.