If the AAC adds Boise, Air Force, and SDSU, it absolutely becomes the top G5 conference and will likely land the NY6 bid 80% of the time. So, BYU affiliates with that conference for some OOC games and bowls...but distances itself by continuing to claim independence and play a P5-like football schedule. 

BYU and Gonzaga join the AAC (along with Boise, Air Force, and SDSU) for Olympic sports. That expanded AAC is clearly a major, multi-bid basketball conference. 

THAT is similar to Notre Dame's prior relationship with the major Big East basketball conference and also reminiscent of Notre Dame's current affiliation with the ACC.

The expanded AAC, as essentially the best-of-the-rest, will continue to gain in prestige and resources and enjoy the label and resources associated with a major basketball conference. While the AAC would still not have a football king, it would be competitively similar to the ACC and PAC 12.