Of course we wouldn't be flung into space by the centrifugal force, magic or otherwise since it has already been clearly established that we are all tied by an invisible string to the center of the earth. Sheesh, get a clue will ya?
The real question is if the invisible rope that is tied to the bucket that holds the earth in the suns orbit were to break, would the earth go careening into alpha centauri way earlier than expected? And if so, would the invisible bucket protect us from other collisions along the way and what would happen if the rope got caught on a quazar or nebula or something?