Was BYU being a part of their conference for so many years helpful to them? Absolutely.
But carried is a strong word. 2004 and 2008 got Utah to where they are today. And 2008 was built on 2004. So really if anything, the hiring of Urban carried them to where they are today.
The relationship and being affiliated with BYU helped, no doubt. But to say BYU carried Utah is a stretch.