Using the Pairwise simulator on College Hockey News, it looks like there's only one game that will determine whether or not Providence gets in.
Both of the teams in the Atlantic Hockey final are below Providence in the Pairwise, so the winner will automatically get the 16th seed in the tournament, and the loser will be done.
The teams in the NCHC and WCHA finals are all top-10 in the Pairwise. Losing today won't drop any of them below Providence, and winning won't push Providence any lower.
Oddly, the Hockey East final will impact who gets in from the ECAC, but won't change Providence's ranking. If BU wins Hockey East, both Colgate and Harvard will qualify. If Mass-Lowell wins Hockey East, then only the ECAC champion will qualify.
Because the Pairwise uses strength of schedule in its rankings, and Providence beat Mass-Lowell both times they played this year, a Mass-Lowell win would boost Providence's score enough to push them ahead of the ECAC loser, who would drop due to their loss. A BU win would keep Mass-Lowell behind Providence and the ECAC loser ahead of Providence.
The game that will determine if Providence qualifies is the Big-10 final between Michigan and Minnesota. Minnesota is ahead of Providence in the Pairwise, and Michigan is behind. Regardless of what happens, Providence will remain as the 15th-highest Pairwise team. If Minnesota wins, Providence will get in as the 15th seed. If Michigan wins, they'll get the automatic qualifier and steal the 15th seed in the tournament from Providence.
Go Gophers!