I'd worry more about being stuck with some generic face model than the beard aspect.
I think that's been my biggest frustration with the game. I'm constantly tuning attributes and sliders in spite of the game. I'm just trying to get it to look a little bit like real hockey, and also make up for the fact that the AI have no idea what to do on the ice.
"Oh, I'm on a two-on-one breakaway with a forward...wait, I'm a defender...I don't break away. Better stop at the blue line and let him go one-on-one instead of get open for the pass and shot."