From men's conference tournament history - maybe not what you were looking for as a comparison ...
To me, it seems like a different sport, at least in terms of considerations like these. Men's teams skate four lines, not in terms of balanced minutes, but much more so than women's teams do once you get to the stage where a loss ends your season. Men's games also have checking. On one hand, it makes the game more physically demanding, but it can also be a way to compensate when you're the team that doesn't have jump that day.
There are a lot of examples in the women's game involving OT in league tournaments. For example, in 2020, UMD and BSU played 10 minutes of OT in game 1 of a quarterfinal series, went halfway through the 4th OT on Saturday, and had to play a third game on Sunday. The Beavers had allowed three goals in 10 periods to that point, but they gave up four goals in ~ 10 minutes in one stretch on Sunday. Those games are different, in that both teams are taxed physically, but emotionally, it gets harder and harder to rally after playing so many minutes where one mistake could end your season.
Look at the results for both SLU and UMD on Saturday. Both came off shutout wins on Thursday, then allowed goals 16 seconds and 22 seconds, respectively, into their games on Saturday. Teams spend a lot of emotional energy in long games, focusing on every shift, every play. It can be hard to reset and bring that same intensity, especially at the start of the next game. Think of playing a video game where the speed/difficulty is ramping up and achieving a personal best. If you start another game immediately after, you can make an error on an easy level, because the concentration just isn't the same.
When players are coming off what may be the longest game of their lives, it adds another wrinkle. Personally, I typically find it more challenging to do something that I've never done before then it is to repeat a past experience.
Anyway, I think it might be difficult for Clarkson early in their game, more than late. Minnesota had games this year against both the Golden Knights and Buckeyes where a two-goal, first-period lead didn't stand up. In the case of tOSU, the Buckeyes had taken a lead by 8:24 into the second period. They're just so deep offensively, that you can't take a shift off. I'd guess that Clarkson is the better defensive team under normal circumstances, but I don't think the Knights can afford to fall behind early this time.