In theory, yes. If a team could win 60% or 70% of their faceoffs over the course of a season, this would be a statistically significant advantage.
The problem is that pretty much every team, every year finishes between 47% and 53% in the faceoff circle. League leaders this year were 54%. And the difference between being a 48% 'bad' faceoff team and a 52% 'good' faceoff team is only 1 or 2 faceoffs/game which in a sport which features literally hundreds of possession changes in a game ... just isn't statistically significant.
Outside of very rare exceptions (and the 10-11 Canucks might have been one of those exceptions) it's just not something you can drive success with. Obviously you don't want to ignore it and you don't want to be at 40%, but it isn't worth sacrificing other aspects of your roster that actually move the needle for a small impact in faceoff%.
This isn't impossible but from what I've seen of Tocchet he's going to want both a high-leverage defensive 3rd line plus a traditional physical/defensive 4th line so I'd be a bit surprised if we see an Adam Gaudette-type 3rd line C usage.
I think the problem is that you're taking raw faceoff percentage over a team across a whole season (which normalizes somewhat) and forgetting that while over a large sample size this might be true, if you put Patrice Bergeron against Jack Hughes 100 times on the draw you're going to see Bergeron win like 88 faceoffs.
So match-ups matter.
Also, overall percentages are misleading because strategies are different in some zones and indeed players don't try as hard in the neutral zone.
I recall reading a story from a high level player during the 60's who said he got all excited because he beat Beliveau like 3 draws in a row in the neutral zone. But when it was a faceoff that mattered he didn't even have a chance.
There's also a false dichotomy here. Nobody is arguing that we should acquire Mike Mcleod because he's good at faceoffs and trade Quinn Hughes to do it.
Also, it's easy to say that it's just a couple of face offs per game, but which face offs? Think of how slim the margins are in this league with billions of dollars at stake?
Having a good face off team versus a bad face off team could be a swing of like 6 wins.
Maybe not in a way that's directly quantifiable by JFresh, but suppose your top D pairing is out there for a minute and a half and then ices the puck.
You have a poor faceoff man out there who loses the draw leading to 45 more seconds of possession and two forecheck hits that exhaust your D.
This might indirectly cost you the game when a faceoff win and an easy change could have allowed your top D pairing to stay fresher and mentally sharper out there..
Just because it's not easily quantifiable by blunt force statistics doesn't mean it isn't relevant.