Exact statistics are hard to find, but given the nature of hockey it's definitely a winning strategy.
One of the key ways to score a goal in hockey is to get shots on net. It doesn't matter if it's a particularly good shot. If a goalie's save percentage is .900, if you get thirty shots there are good odds you'll score 3 goals, whether they're flukey or artwork.
And one of the more sure ways to get shots in hockey are either odd-man rushes where players have lanes to put the puck on net, or when they have a man advantage and a player can get into empty space. This is why the power-play, and being short-handed are often central to hockey strategy. If you can group 5 really good players on a powerplay against a team with weak special teams, your odds of scoring increase by a huge amount.
This line of thinking also applies to pulling the goalie. When there are six attackers versus five defenders, the attacking team has far better odds of scoring a goal due to increased shooting lanes and an easier time retaining possession. When at even strength they might be lucky to get one quality scoring chance in 2-3 minutes, with an extra attacker they might get three or four, or even more.
In other words, if they pull the goalie there are much better odds that they'll score a goal, if they don't pull the goalie there are much better odds that they won't score a goal. Since a goal is what they need, pulling their goalie is a good idea.