How important is it to have a Group A Lens for Canon?

With my new Canon 5D3 I see that now lenses are put in groups from A through H.
Am I more likely to get a bird in flight in focus if I use a Group A lens instead of a Group C lens?

For example would the 400mm f/2.8 II (Group A) give me more in focus pictures of birds flying than the 400mm f4.0 DO (Group C)?
If there is a difference, roughly how much of a difference would it make when photographing birds in flight? Twice as many in focus?

If I put a 1.4 teleconverter on the 400mm f/2.8 II it becomes Group C.
Would the AF then be essentially equivalent with the 600mm f4L II (also Group C)?
In other words, would the AF speed and AF accuracy then be about the same?

Thanks for any insight into this!
Henry

Henry, where are you seeing these groupings?

Artie, The Lens Groupings are listed in the Canon 5D3 Owner's Manual between pages 79 and 84.

Thanks Henry. I have never once concerned myself with any such info. Especially cross type sensors and the like. It there was a way to create a test to measure any differences I know that the following would be true: skilled flight photographers would make a higher percentage of sharp images with any combination of camera bodies and lenses than unskilled folks would make with a 1D X and the whatever the "best lens" is supposed to be.... Guaranteed.