The Conn Smythe is almost always a member of the Stanley Cup-winning team; Jean-Sebastien Giguere of the 2003 Mighty Ducks of Anaheim was the last to win it without also hoisting the Cup.
It's also possible for a member of the losing team to win the Conn Smythe Trophy ... including the most recent (Jean-Sebastian Giguere in 2003), it was awarded to the opposing goalie.