Yes it matters. . .
Does it really matter? Not really. . . Only if the Big12 Screws the pooch like Pac12 did and goes like 15 bowl game losing streak . . . which even that didn't really change much.
As for a BYU brand perception. . . conference affiliation has an impact, but our brand is based mostly on whether BYU wins and loses. . . The loss for West Virginia last night had minimal impact on BYU's brand.