He won't because that's not what any of the appeals or potential litigation are over. NFLPA doesn't seem to be appealing the suspension (as I understand it), but rather challenging that Troy Vincent is even allowed to give the punishment to begin with, and that that is a commissioner power that cannot be delegated.
Arguing over technicalities rather than the case.
The PA is actually appealing the suspension on multiple grounds, you are right about them challenging Vincent handing down the suspension, but also the Wells report itself and precedent of punishment.
Unless the arbitrator knocKS this to 0 games, expect this to end up in federal court.