OK, this is one of those questions that Turbine needs to research.
Here's the situation. LSU looked down their noses at Cajun culture forever. Or at least, until it became internationally exciting, and then they tried to convince everyone they are the Cajuns (while, of course, still looking down their noses at us.) And we know that LSU is not very original in much of anything they do. Face it, they got their school colors because the local hardware store only had those colors of ribbons in stock, and even their fight song is taken from an old Broadway musical.
Finally, I doubt that anybody over there much knew what Boudin was until the past few decades, and I doubt they ever knew what couche-couche was.
When I was a cheerleader in 1980, I put together an upbeat version of 'Hot Boudin.' We went to cheerleading camp and LSU was there. When they heard it, they insisted that that was their cheer.
Again, I don't have any evidence, but for the preceding reasons, I doubt it. I suspect it has been part of our traditions for decades, and it is probably printed up in an old yearbook, or maybe a Vermilion.
I gave Turbine a lot of old yearbooks.