Yes.
I don't know the process, however. Each time a current or former military person gets to be "it" and carries the flag away escorted by Disney's own people.
It is really, really cool and they have a photo session with the flag and the military person's family.
I've seen it with current marines, former servicemen, and this really, really fun guy from WWII. I think he was so excited to be picked, he jumped and clicked his heels, or did some sort of dance step.