IMHO, the advanced degree you are considering will not be useful for the following reasons:
1) unless you plan on finishing it BEFORE you start medical school, it may actually hurt you to apply to medical school with the plan of dropping out of the graduate program. Medical schools do not like "stealing" students from other programs and it will appear as if you don't finish what you start.
2) it won't make a bit of difference in obtaining a residency program down the line. If you are considering a competitive speciality or an academic practice, medical research may come in handy and would be a nice kudo on your residency application. However, the MAJOR determinants of residency placement are USMLE, med school gpa and letters of recommendation. Things like AOA, research, extracurriculars and connections will be of value in varying degrees at varying programs.
My advice is to go ahead and get the advanced degree IF it interests you and you are planning on finishing the program, but don't do it if you are only doing it to bolster your application - it won't help much, if at all come residency time.
Best of luck.