Yes; also. Because the cup provided additional memories, not competing ones.
Not for me. I barely remember the relegation fight (or the mullering). But that's beside the point. We didn't drop into danger because of the cup competition. We did that because we had a poor team and a poor manager.
It's not either/or. We could have had both.
It's not all about money and media attention though. When we look back at the 2008/09 season, we tend to think of the penalty shoot out win v man city. We don't remember how much money it brought us, or what the press said. We remember the elation...