Big caveat here: I honestly don't know.
Having said that, I'll make an educated guess: Consultancies want the best people, but don't have/take a lot of time to review resumes and letters thoroughly. If you show a 2.4 GPA, this might be the end of your application. I'd probably remove the grades that you obviously failed / did worse in BECAUSE of the emergencies.Second big caveat though: make it very clear you are doing this, probably exen explain what your GPA would be if including these grades. I would also preempt and have an explanation from counselor, surgeon, ... ready without the consultancy requesting.
PS: I read long ago an amazing essay from a Harvard MBA applicant explaning why he was out of work for a year while taking care of his ailing gd-mother. Rather than hurting him, this essay may have been the most amazing part of his particularly strong application, and he got in the program. Hopefully you can turn your physical bad luck into a strength on the application.
Fellow Current/former consultants, I am curious to hear your recommendations. Anyone strongly disagree w/ my take here?