That would be akin to giving up, a fireable offense in the coaching world.They wouldn't "have" to pull the goalie. They might, but wouldn't have to.
If the only way you can make the playoffs is a regulation win against the team your playing against, then you do everything in your power to win in regulation. Which means if you're tied near the end of regulation you are pulling your goalie.
Winning in OT means the same as losing in regulation, you HAVE to pull your goalie in that situation or you shouldn't be making those types of decisions.