The way it will work is, the job will be open for applications, there will be interviews with a panel, the Chancellor of the Duchy of Lancaster (Pat McFadden) will decide on his preferred candidate, and the PM will have to agree.
Because this is a significant appointment that's supposed to be independent and hold the government to account, there will be a pre-appointment hearing with the Women and Equalities Committee where the preferred candidate will be questioned on their fitness for the job.
As I see it, if Harman applies she would on the face of it be a very credible candidate. So what it will come down to is either there's a stronger candidate or Pat McFadden and/or No10 spads decide she's too controversial a proposition.
So it might be best to game out what happens if she does get it. And there I think she might be constrained. She might fudge guidance, but actually going against the SC would be highly risky for her.