They have embeding disabled, but just click here to see it.
The uniforms are not the band's real uniforms of course - except for the drum major's. I'm pretty sure they just put white tape over "IRISH" on the sleeve cuffs.
Apparently the band found the following performance of their song "Here it Goes Again" on YouTube. They loved it so much they decided the Band of the Fighting Irish would have to be a part of a future video.
One of the band directors, Matt Merten, has posted this clip from a local new channel detailing the story. Laura Taylor, band member and current Notre Dame Tridentine Mass community secretary, gets a nice little spot.
P.S. John Nagy also has an article up on ND Magazine about it. Read that here.