Probably not. The reason is that as you get the top teams playing each other in the tournament, both teams often have very good goalies that stop almost all of the shots. The exceptions become shots that are screened or pinball around, or a perfectly executed two on one or other backdoor feed.
There aren't that many goalies that have won two NCAA titles: Sautter, UMD; Horak, UM; Vetter, UW; Räty, UM; Leveille, UM; Tiley, Clarkson. Only Vetter won three. A lot of great goalies didn't win any despite playing for excellent teams.
Another thing to consider is that it can be a totally different challenge for a goalie when seeing 20 shots per game rather than seeing 50. If she sees only two shots in a period but one hits the net, that can be more damaging than when one of 16 shots in a frame connects.