The question of whether or not BYU becomes an independent should be answered sometime today or tomorrow, and all indications point to them remaining it the Mountain West. But..... that is no fun to think about.
If BYU were to become an independent in football, should the Pac-12 incorporate BYU into their bowl affiliations, similar to how Notre Dame and the Big East are affiliated for bowl games. I would assume the Rose Bowl would be exempt from any potential agreement, thus the Pac-12 will continue to send their conference champion to LA, unless they are selected for the national championship game. BYU would then be eligible for the remaining bowls (Alamo bowl through the Vegas bowl).
BYU has a massive following and represents extremely well at bowl games. Warning, I don't have evidence, but I would guess BYU would consistently sell more tickets to the lower-tier bowl games than Washington State, Oregon State, Stanford, Arizona, & ASU. In fact, the only teams I would guess would consistently out sell BYU are Washington and Oregon. Furthermore, the Pac-12 bowl cities of San Diego, Bay area, Las Vegas, and Texas all have large Mormon populations. BYU increases the potential for ticket sales for the non-Rose bowl bowl games, thus increasing the value of the Pac-12 tie-in, hopefully generating more money for the league.
BYU would be interested because as an independent they have no set bowl games, relegating them to either a BCS bowl or a substitute for a league that was unable to fill its bowl eligible quota. The Pac-12 can also offer better bowls than either the WAC or the Mountain West, and as previously mentioned each of the bowl sites have sizable Mormon populations.
Potential Ulterior Motives:
A final point, I don't know if the Pac-12 is better served with the Mountain West gaining a BCS bid or not. The two conferences schedule a lot of games together, and therefore we would receive a perception boost from playing more BCS-level schools. But, recruiting might become more difficult, as we have to battle 10 new bcs schools in our region. At the same time, I can't imagine Colorado losing recruits to Colorado State, UCLA losing recruits to San Diego State, or Cal losing recruits to Fresno State solely because those schools are now in an AQ conference. Regardless, aligning with BYU for bowl games, decreases the chances the Mountain West receives an auto-bid to the BCS.
I lot of the issues that would have arisen with BYU being a conference member, oversaturation of the Utah market, no-play on Sunday, and cultural differences, would not apply to the bowl affiliation.