If you're a long-time reader of this blog, then you probably know that my least favorite team is the San Francisco Giants (I like them even less than the Florida Panthers). As the 2011 Giants implode in front of their disbelieving fans, I wondered if any NHL teams with San Francisco's signature talent - being the worst offensive team in the league - had ever been successful.
I went back to 1967-68 and looked at how many teams with the worst (or second-worst; the Giants might finish 2nd-last) offense in the league made the playoffs, and how they did in the post-season. Overall, 9% of last-place offensive teams made the playoffs, and 20% of second-last-place teams secured a playoff berth. That's 13 teams overall; five of these "successful" teams did it prior to NHL realignment in 1974 coming from the expansion division, so we'll ignore their results.
That leaves eight teams:
It's sheer coincidence, but Glen Hanlon was the backup goalie for three of these teams and Steve Weeks was for two. At any rate, aside from the 1978-79 Canucks, these aren't terrible teams - they went 6-7 in playoff series, outshot their opponents by roughly 100 shots and their average goal differential was -8; the teams that finished last in the league offensively and didn't make the playoffs were -81 in the goals department.
That leads to something important: since 1979-80, only three teams have posted a positive goal differential while being last or second-last in the league in goals scored: the 85-86 Rangers, the 95-96 Devils (who missed the playoffs) and the 09-10 Bruins. You have to get a bit unlucky to finish last in the league in goals, but as the shot differential indicates, these teams weren't that unlucky since they won enough games to make the playoffs. Rather, they were the extremely rare teams that were so oddly-constructed that they simultaneously had the best defense and goaltending in the league and no offense to speak of. The 1998-99 Stanley Cup finalist Buffalo Sabres are remembered for having no offense - they were 17th in a 27-team league; the last and second-last-place teams didn't sniff the playoffs.
So no, it isn't really possible to be successful in the NHL with the league's worst offense. Same goes for baseball.