Has a Copa America game ever ended 6-3?
Exactly once. On January 14, 1945, Chile beat Ecuador 6-3, and no Copa America game before or since has ended that way. When it happened it was a scorigami, the first 6-3 in league history.
That makes 6-3 the 26th most common final score out of 36 that have ever occurred in Copa America. One point away, 7-3 has happened never and 6-4 has happened 1 times.