I read in one of the posts that the 1Dx will achieve a quicker autofocus time than the 5DIII because of the extra battery power.
This discussion I believe was in relation to the 85 1.2 which is known to autofocus slowly.

Question:

Will adding a battery grip to a 5DIII have an affect on the autofocus speed.
I realize that this is largely lens dependent but the idea of the extra power does beg the question.

Thank you.