I know it's a joke but players and teammates absolutely do care about guys reaching milestones or chasing personal awards, especially at the last couple games of the season. The whole team pretty much stopped trying to score and kept feeding Stamkos for that 60th goal, Ovechkin has entered the final games of the season just shy of 50 goals and the whole team just feeds him endlessly. I've been told by relatives how bad the Jets wanted Selanne to beat Mogilny in that 76 goal rookie year, he needed a hattrick in the final game to win it and only ended got 2 resulting in the tie, every 2nd pass was trying to hit Selanne.
So yeah we might see some extra deference/sloppy play from guys trying to hit Kucherov which is ironic because he could probably sneeze out 2 assists if everyone just played normally.