The designed car will stay attached to your band or car for "a while". I can't say how long that is, but I haven't had it carry over from one trip to the next in the couple of times I tried. So they do seem to flush the design cache at least every few months. I would guess quite a bit shorter than that.
One thing to note is that this is a case where the design is associated with the actual individual band/card, and not with the MyDEx account itself. So if he had multiple bands/cards, he could actually have more than one car saved in the system. They would each appear if he tapped his cards one at a time in the post-ride area where they display the top cars of the day.
I'm going to experiment on my upcoming trip, but I suspect that any RFID card, such as my Washngton DC Metro card, may work for purposes of designing a car.
Finally, be aware that there are two car design stations in the post-ride area that can be accessed at any time, without having to ride the attraction. One possibility is to hit that station, design a car taking as long as he wants, and then hitting single rider without tapping his band at the design station inside the queue.