To an extent, yes they do. If the NHL is to agree to participation, they will be looking for world exposure as one of the benefits. Obviously money is the other (see World Cup = money grab).
There won't be a lot of money to be made by the NHL with only a hypothetical 4 games in Canada/4 in Russia......especially when few people in America will care about such a series.
Actually it's more than 'to an extent'. All players in the NHL are under contract for the full year, not just during the hockey season. So for a player to play for somebody other than their club team (such as their national team), they need to get permission from both their team and the league.