Has a Copa America game ever ended 4-3?
Yes. Copa America has seen a final score of 4-3 7 times. It first happened on October 29, 1923, when Argentina beat Paraguay, and most recently on March 31, 1963, when Ecuador beat Colombia.
That makes 4-3 the 18th most common final score out of 36 that have ever occurred in Copa America. One point away, 5-3 has happened 4 times and 4-4 has happened 1 times. Nearly all of its occurrences fall between 1920 and 1949.