Has an International Rugby game ever ended 31-3?
Exactly once. On January 20, 1912, Scotland beat France 31-3, and no International Rugby game before or since has ended that way. When it happened it was a scorigami, the first 31-3 in league history.
That makes 31-3 the 510th most common final score out of 844 that have ever occurred in International Rugby. One point away, 32-3 has happened 3 times and 31-4 has happened never.