HR does not have a decision mandate beyond the stage where candidates are invited to interviews. From there on, HR is responsible for facilitation and ensuring a smooth process for all candidates, independent of whether they eventually get the offer or not. However, as Bruno said, HR might influence the decision in rare cases when candidates exhibit inappropriate or rude behavior. But this is extremely rare - so in 99 out of 100 cases, HR effectively has no say.
Does HR have a say after all consultants confirm to make an offer to a candidate?
At McK, actually the HR facilitate the discussion with all the interviewers that led to the hire or not (Or in pass or no in R1) decision, so in fact it can contribute for the discussion. But it’s very rare that they will have a very active role, and often only work as facilitators - that said, if someone screws really bad with HR (eg, disrespectfully behavior) they risk to lose an offer even if have outstanding interviews
HR does not participate in making a hiring decision. Although HR will check your transcripts at some point. Usually, this happens after you get the offer.
Confirm what others have said: not an active role, just facilitates discussion among consulting staff.
Hope it helps,