The old adage in some sports is that if you don't win Game Six, odds are you won't win Game Seven. In some cases that is true and many teams do try to close it out in Game Sixes. Yet, since the seven-game series format has come to the NHL in the 1939 Stanley Cup finals, that hasn't always been the case.
It should be noted that I hate research and often have issues with it-- so when you get the misinformation in this and want to correct it, the comments section is the place to do it. If anything else, I'll chalk it up to tiredness and not wanting to be thorough.
Since that, there has been 15 series' that have gone the full seven games and in seven of those series have the team that has won Game Six went onto win the Series: 1942 Toronto Maple Leafs, 1950 Detroit Red Wings, 1964 Toronto Maple Leafs, 1971 Montreal Canadiens, 2001 Colorado Avalanche, 2004 Tampa Bay Lightning, and 2009 Pittsburgh Penguins.
Of the eight teams that didn't win a Game Seven after a Game Six win, only the 1994 Canucks scored more than a goal in their Game Seven loss. The rest of the teams got shutout or only put up one goal in the final game.
So, with about 47% winning a Game Seven after winning a Game Six, then only 20% of teams winning a Game Seven on the Road; the odds are slightly in favor of the Canucks and could prove that home-ice advantage is nothing to laugh at, especially with the home team winning the six previous games in this series and in 41 of the previous 82 playoff games this year, excluding the Finals games.
Good news for the Canucks though-- only the 1945 Toronto Maple Leafs, 1971 Montreal Canadiens, and 2009 Pittsburgh Penguins have won Game Seven on the road.