I don't even care if they faked the timing or edited multiple takes together, I'm just happy that it exists. They also have a marching-band video version of this song which is somehow even cooler.
[Check out this interview to learn a bit about how they did it. Apparently they did several full takes, but none was perfect so there is one splice in the video. Also apparently the timing wasn't faked, although they did speed up and slow down the video by small amounts in places.]