Has a Copa America game ever ended 11-0?
Exactly once. On August 10, 1975, Argentina beat Venezuela 11-0, and no Copa America game before or since has ended that way. When it happened it was a scorigami, the first 11-0 in league history.
That makes 11-0 the 26th most common final score out of 36 that have ever occurred in Copa America. One point away, 12-0 has happened 1 times and 11-1 has happened never.