Has a Copa America game ever ended 6-4?
It has. 6-4 has been a Copa America final 2 times in 1,738 games. The first was Brazil beat Chile on January 3, 1937; the latest was Brazil beat Chile on January 3, 1937.
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.