When I toured TMMK, basically I watched cars roll off the end of the line regularly(I think 45 seconds or so on the Camry line at the time). They'd get started, and provided nothing major happened at start as I understood it from there most of them went straight on to the truck to go to the dealer.
If something was amiss after starting, or sometimes just as a quality check, cars would get put off to the side where they'd either be taken out back and driven on the track(assuming nothing was wrong and it was just a random sample) or they'd be worked on and then driven.
I'd GUESS the ones that were driven/worked on probably went on an alignment rack if there was a reason to think they needed to. Most of them-there wouldn't have been a chance to do it.
I'd be interested too if certain cars get more attention than others. As an example, if you took factory/NCM delivery of a Corvette, I'd think they'd go through and make sure it was as perfect as they could before you picked it up. It wouldn't exactly look great for the people touring the museum and watching you pick up your car to see you have issues like obviously bad alignment when you drove it off. Plus, I think the presumption is a lot of people are going to take delivery and then go out and drive the snot out of the thing right out of the gate.