Jordan Staal scored twice, including the game-winner, as the Hurricanes defeated the Golden Knights 5-3 in Game 4 to even the Stanley Cup Final at 2-2.
Russell has failed to score in the previous two rounds.
The third major of the year starts on June 18 at Shinnecock Hills.
Any decision to give Itoje the summer off would be in recognition of a demanding year.
England have faced accusations of wilting when matches are on a knife edge in more recent tournaments.
Rashabar carried the famous Sangster silks to an emotional success under Loughnane.