Here's a great case study I noticed when I lost my CT final.
American U: 24-5 (13-3 conf,) conf champ, 9-1 last 10, 11-3 road, 0-0 against top 25, 3-1 against RPI <50, RPI 41, SOS 148, not ranked
U of Vermont: 24-5 (14-2 conf,) conf champ, 9-1 last 10, 11-2 road, 0-0 against top 25, 3-3 against RPI <50, RPI 24, SOS 83, rank 33
Both teams received an 8 seed. So with very similar résumés (except for the RPI) resulting in the same seed (Vermont's was with the #4 1-seed, Am U's with the #1 team,) it seems safe to conclude:
Winning your CT final can make up for about 15 points in the RPI when it comes to seeding in the NT.