Does Leonin Arbiter affect Karn, The Great Creator from choosing a card outside of the game?
No, Leonin Arbiter has no effect on Karn's ability. The library is a specific zone in the game; it is where you put the deck to start the game, and it is where you draw cards from. The sideboard is a completely separate thing outside of the game; it is normally used for switching cards into and out of your deck between games in a match, and only specific effects like on Karn can access it during a game.