For sure. Come Selection Monday, we might know LSU's exact ranking (among the Top 6-16 teams. But, we'll for sure know if they are on the 2-line or the 3-line. And, we already know they won't be in the Greensboro regional with South Carolina.
Based on this week's upset losses, the committee could make their own lives easier (not having to deal with 4-teams from the same conference among the Top 16 seeds) by simply pushing Oklahoma (lost to Kansas), and Maryland (lost to Indiana), etc. out of the Top 16 (they were pretty marginal already in Monday night's reveal).