I do not think so. I practice daily not to divert my eyes back to the barrel. I do this everyday because if I do not, my eyes will always go back to the barrel.
I do not think the brain does this magically. It's hard work.
Ok then, if your eyes are locked on the bird as you say and you don't think the Brain is playing a key factor, how are YOU attaining lead? Explain...
Secondly, of course hard work is part of it. But don't underestimate the power of the Brain. In Sporting Clays, once you call for the target you've hopefully already formulated a plan, your thinking is done and you simply let it happen, you let the mind take over. The only thing you should be concerned with is seeing the bird as clear as you can just before the shot is triggered. I know it may sound hard to believe, but it works if you trust it.
Now we've been relating more to clay shooting and Hunting is certainly more instinctive because we don't know when, where or what angle the bird might come from, but the concept of hard focus and the ability of the eyes leading the hands (Gun) to the bird is quite the same whether hunting or shooting clays. Subsequently, we've all heard someone at some point in time describe the shot they made of a lifetime on that goose, Duck or be it a Pheasant. If you ask them
"how far in front of that bird were they", most times they can't answer it because they honestly don't know. They pulled up, focused on the birds head, pulled the trigger and the bird fell out of the sky. Amazing what that thing called a "brain" can work out when the eyes give it the correct info.
I will try to find some info written by fellas that teach this kind of stuff for a living and can explain it better than I.