Yes!
For residency candidates: The NRMP Program Directors' Survey makes it very clear that interviews matter a lot, which was also my experience as an Assistant Residency Director. I recall very robust conversations about even small comments candidates made during their interviews, some of which affected their ranking on our Match list.
For medical school applicants: Although there is controversy over how much college interviews matter, even skeptics acknowledge that graduate school interviews make a difference in the application process. In this NYT piece, two former interviewers strongly advise conducting mock interviews and being prepared for "curve ball" questions.
Remember: If you're well-prepared, once you get your foot in the door, you can make a strong impression about the worthiness of your candidacy.
