Has a Copa America game ever ended 6-4?
Exactly once. On January 3, 1937, Brazil beat Chile 6-4, and no Copa America game before or since has ended that way. When it happened it was a scorigami, the first 6-4 in league history.
That makes 6-4 the 26th most common final score out of 36 that have ever occurred in Copa America. One point away, 7-4 has happened never and 6-5 has happened never.