I applied at the end of my undergrad, and did not get in. I since enrolled in a Master's of epidemiology (which I have loved, btw). I am currently holding two acceptances, and am waitlsited at a third school. I do think a graduate degree can help, but there's a few caveats:
1) As an international, I was much better at picking my schools accoridngly the second time around, and much better with timing my application.
2) The last time I applied, the schools never saw my senior year GPA. With that year, my undergrad GPA was much higher (as are my MCAT scores). My graduate GPA is even higher, but I am unsure as to the degree that grad courses matter for med school applications.
3) Since I am involved in clinical research, my grad degree added to my application in less direct ways as well. It allowed me to have a publication, to submit letters of references from physicians (my supervisor is a doctor), shadow physicians, and have a lot of patient contact for my research. Obviously, not every graduate degree can provide these opportunities.
I would also add that my research experience tends to be more well-regarded at schools that are more research focused. In general, a relevant graduate degree may add more to your application at schools that whose mission is in line with your grad degree, and may not have as much of an impact at other schools.
