I think it has potential to develop into a rivalry but right now, I wouldn't officially call it a rivalry.
For one, the teams are in separate conferences. Unless they meet in the Stanley Cup Finals, they will only pay once a year at most. Makes it pretty difficult to have a good rivarly if the teams barely play.
Secondly, for a rivalry to truly be born, something bad or controversial has to happen typically. Someone needs to injure somebody, some sort of controversial goal, fight, trash talk in the media, etc. Once that happens, a rivalry is born.
The two team are both excellent teams and that is one factor they have going for them. Usually when teams don't play each other a lot, a rivalry can still form if the two teams are both really good and constantly meet in the playoffs. IF Vancouver and Boston meet again in the Finals this year, then I'd say it's a bonafide rivarly. Let me give you some examples:
Detroit-Colorado (mid nineties to early 2000s): This rivalry was one of the best rivaries in recent years. The Wings reached the Stanley Cup Finals in 1995 only to be swept by New Jersey. The following year, the Wings had the best record in NHL history 62-13-7 but they were eliminated from the playoffs in the Western Conference Finals by Colorado. In that series, Claude Lemieux delivered a dirty check to the Wings' Kris Draper causing severe injuries (including a broken Jaw). The following season, when the two teams played at Joe Louis Arena, a bench clearing brawl ensued when Darren McCarty started punching Claude Lemieux during a stopage. Even the goalies ended up fighting at center ice. The two teams would meet again in the West Finals with the Wings defeating Colorado in 6 games to advance to the Stanley Cup Finals (which Detroit ended up winning). Detroit won the Cup the following season and Colorado went on to win another Cup in 2000. The teams met again in the Western Conf finals in 2002, a series which Detroit won in 7 games.
The rivalry gradually died out as Colorado faded, although the teams would meet again in the 2008 playoffs, in which Detroit won in a 4 game sweep.
Detroit-Pittsburgh: These two teams have a cross-conference rivalry. This is what Boston and Vancouver could become. The two teams met in the 2008 Stanley Cup Playoffs in which Detroit won in 6 games. They skated the Cup around on Pittsburgh home ice and this enraged many of the Penguins fans and players. The Pens vowed revenge and they got it the next year beating Detroit in 7 games and skating the Cup around the ice at Joe Louis Arena. Sydney Crosby created controversy when he didn't shake the hands of the some of the Wings players including captain Nick Lidstrom. Interestly Marion Hossa played for Pittsburgh in 2008 so he didn't win the Cup that year. The following year he played for the Wings and he didn't win the Cup that year as he again lost in the Finals. He would go on to win the Cup the next year with Chicago.
THAT is how a rivalry is born, between two teams in opposite conferences. Play consecutive years in the playoffs and cause some sort of controversy so the opposing fans and players hate each other.
Some other Detroit related rivalries: Wings- Blackhawks(Two Original Six teams that play each other multiple times each year. Both teams hate each other and both cities hate each other).
Detroit-Toronto: The teams don't play much any more but they have a rich history having played each other multiple times in the playoffs and regular season. Two the league's oldest teams.