Here are ND's game-by-game face-off stats:

Georgetown: 17/22 (77.3%) - Won 12-7
Bellarmine: 11/20 (55.0%) - Won 11-6
Detroit: 15/22 (68.2%) - Won 14-5
Maryland: 9/17 (52.9%) - Won 9-4
Denver: 9/21 (42.8%) - Lost 9-8 (OT)
Virginia: 4/18 (22.2%) - Won 8-7 (OT)
Ohio State: 8/21 (38.1%) - Won 9-8
Syracuse: 15/27 (55.6%) - Won 17-7
Duke: 7/18 (38.9%) - Won 8-6
Marquette: 13/18 (72.2%) - Won 8-7 (OT)
North Carolina: 16/35 (45.7%) - Lost 17-15
Duke (ACC): 5/23 (21.7%) - Lost 10-9 (OT)
Army: 12/24 (50.0%) - Won 13-7
Air Force (NCAA): 17/26 (65.4%) - Won 15-7

As you surmise, ND's face-off performance in its losses was pretty horrible. Likewise for a couple wins against lesser foes (UVa, OSU) that were closer than they should have been. The biggest outliers appear to be the wins over Duke and Marquette. Against Duke, ND got killed at the X yet still won, which suggests that Duke's early exit from the NCAA's probably wasn't a fluke. Against Marquette, ND dominated face-offs yet still had to go to overtime.

As presented, we don't HAVE to win FOs to win the game, but man it sure helps. I was actually expecting our FO % to be a bit better against Cuse. It's good, but it shows we might be able to lose the FO battle with them and win.

I didn't get to see the UNC game, and most here were pretty disappointed we let that one slip away. Coach Corrigan as well. Had we gone at least 50% in that game, there is a good chance we would not have lost.

I think the data also supports the original poster's point. Perhaps we should look quite heavily at getting some FOGOs a LOT of practice and instruction with faceoffs over the summer.