I'm not so sure. I suppose they could have the character of Gary Mitchell be a friend of Kirk's, and then give Mitchell a plot that has nothing at all to do with the events surrounding WNMHGB.
You're right of course. But if Cumberbatch is playing Mitchell, then there has to be an explanation of why a human is seemingly giving the much stronger Spock a run for his money.
While there are many possible explanations, the simplest one is that they're using Where No Man...
as a template for the new film.