The short answer to your first question is: Yes, it is possible to achieve different (and perhaps better) results through calling your own plays than through game-plan setting.
I have called most of the offensive plays in a 35-year career (save for most preseason games and the occasional blowout). In playcalling, it matters who you call the play for and where you send them. Better players perform demonstrably better in specific situations. I'm sorry that my evidence is only anecdotal and conclusory---I don't know what I could say that would substitute for the experience of calling your own plays game after game and learning that way.