Has a Copa America game ever ended 6-3?
Yes. Copa America has seen a final score of 6-3 2 times. It first happened on January 14, 1945, when Chile beat Ecuador, and most recently on January 14, 1945, when Chile beat Ecuador.
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 2 times.