First off, let me say AGAIN that batting order doesn't make that much of a difference. Fans fret waaaayyy too much over some batter hitting in the 3 hole versus the 4 hole. Switching your #2 and #6 guys would make a difference of 2 runs over the entire season.
A mistake as egregious as putting a weak hitting pitcher in the cleanup spot and putting your clean up hitter 9th would make a difference of 16 runs over a season, but no manager would do something like that.
The difference between the optimal lineup and a traditional lineup is about 15 runs over a season, 1 or 2 games. Not a huge amount, but nor is it insignificant.
That said, no manager is willing to buck conventional wisdom and put someone like Youkilis in the leadoff spot. Therefore, the types of changes that we are talking about in the lineup are negligible. Therefore, let me say AGAIN, that a manager is better off putting hitters where they feel most comfortable. In other words, sabermetric folks recommend that managers go with the human element/dynamics thing.
Now if there is a manager out there who IS willing to go against traditional wisdom and set a line up correctly, then that's a different story.