I don't believe they would.
History shows that they have a previous in not conceding anything .
Found this article from 1986. Hearts needed 5 points from their last 3 games to win the league. The sheep & the arabs ( we were nowhere & fighting off a challenge from Dundee to be 5th) had conceded , but that horrible barsteward Davie Hay would not. He was mocked , but we all know what happened in the end. As Hay said "You never know in football".