Byu has been pretty shaky in ncaa tournament first round games, but a lot of that seems to do with seeding. In fact, they have actually never lost in the first round when seeded 7 or better (5-0) So your scenario is worse than their history.
1981 6 seed, beat princeton.
1988 4 seed, beat Charlotte
1993 7 seed, beat SMU
2010 7 seed, beat Florida
2011 3 seed, beat Wofford