Has a Copa America game ever ended 4-4?
Exactly once. On March 10, 1963, Bolivia and Ecuador drew 4-4, and no Copa America game before or since has ended that way. When it happened it was a scorigami, the first 4-4 in league history.
That makes 4-4 the 26th most common final score out of 36 that have ever occurred in Copa America. One point away, 5-4 has happened 2 times and 4-5 has happened never.