Here's how it shook out the other two times the Sugar and Rose were semifinals:
2014
Sugar (semi): #1 Alabama (SEC #1) vs #4 Ohio State (B1G #1)
Rose (semi): #2 Oregon (P-12 #1) vs #3 Florida State (ACC #1)
Cotton: #5 Baylor (Big 12 #1) vs #8 Michigan State (B1G, at-large)
Peach: #6 TCU (Big 12, at-large) vs #9 Ole Miss (SEC, at-large)
Orange: #7 Mississippi State (highest remaining SEC/B1G team) vs #12 Georgia Tech (ACC, contractual)
Fiesta: #10 Arizona (P-12, at-large) vs #20 Boise State (G5, guarantee)
2017
Sugar (semi): #1 Clemson (ACC #1) vs #4 Alabama (SEC, at-large)
Rose (semi): #2 Oklahoma (Big 12 #1) vs #3 Georgia (SEC #1)
Cotton: #5 Ohio State (B1G #1) vs #8 USC (P-12 #1)
Orange: #6 Wisconsin (highest remaining SEC/B1G team) vs #10 Miami (ACC, contractual)
Peach: #7 Auburn (SEC, at-large) vs #12 UCF (G5, guarantee)
Fiesta: #9 Penn State (B1G, at-large) vs #11 Washington (P-12, at-large)
If not in the top 4, the Big 12 champ will still be guaranteed a spot somewhere as a "displaced champion." Any other Big 12 team would need to be in the top 12 (probably top 10, in reality) to get an at-large NY6 spot.