I think that your medical school alumni status will be important in a couple of scenarios. First if you want to go into academic medicine and do research, going to a ranked school will be important. Academics love the pedigree as a measure of their ego.
I think that a competitive residency will be enhanced by what school you go to. Just like undergrad, there is a perception, right or wrong, that Harvard students are smarter, even if their stats do not support that.
Finally, if you wanted to be a chief of medicine, or chief of a medical division, going to a ranked school will help.
That being said, it really doesn't matter to me, since I do not desire any of the above, except I would like to be able to choose a residency based on what I want to do, rather than who will admit me into their program.
Finally, your patients won't care where you went to med school. Going to a ranked one will only impress your physician colleagues.