Assuming they ever can string together wins, they'll immediately be afforded the bias that other bluebloods enjoy and that teams like BYU and Utah don't.

Why is this? History. A room in Lincoln full of trophies and legends.

I don't know how long it would take for that to erode to the point that they aren't blueblood anymore. Probably enough time that the people who lived through their greatness are all dead. They won a NC in the 1990s, so that will be a while.