galvonager,
I think part of the answer is in the answer to the question "how long does it take you to say ""OH SH!T"" ?
I'm serious. You've got to see first, and then assess.
That's at least a second gone (say "twenty" once.. under those circumstances seconds are very long...).
After that, whatever you do, push or pull, the aircraft you're flying DOES have a certain amount of inertia.
If you were not exactly on those birds' trajectory... you'll miss them. If you were, anything you will have done on the controls in the two remaining seconds before you hit them will not have made the slightest difference.
I often wonder here, how many people have counted "twenty, twenty, twenty" to roughly count off three second and have understood how short (or long) it can be... before answering certain posts?
CJ