But, i doubt it, as those games usually start at 7pm ET which is 2am in Finland, just as those bars as closing (Sports Acad 3am). Im sure there will be a couple of 'local' bars around the centre that could show it too, but the time will again be the problem - i dont see many still being open at 5am when the games finish!
What hotel are u staying in, maybes they have Viasat hockey channel?
Im sure the hockey on the ice will be good enough for you? are you waiting for individual tickets sales or have u been ripped by a package deal?
Aussie Bar and Elmo bar & Grill both opened at 6 AM to show rugby world cup games and I believe some bars have been open during the super bowl. So I wouldn't be too surprised if they would do the same thing with NHL playoffs, or at least some games.