Very few, if any, Thrifty locations have an aisle where you pick up your car from, so you'll be assigned a car by the rental agent. Therefore, Wild Car and Blue Chip aren't mutually exclusive.
Most Thrifty locations have (and are required to have) a separate Blue Chip line that should theoretically have no line (or at least a shorter and faster one). But because unlike National and maybe Hertz (no experience with them), you don't sign a master rental agreement when signing up for the program, for legal reasons, you still have to sign a rental contract when renting under the Blue Chip program, and so therefore you must visit the rental counter before picking up a car.
I've never found it a hassle and it can be a quick process when it's done right.