Thanks for your thoughts everyone! To clarify, I'm not applying to the M.S. program to strengthen my application, per se--I am really applying because I am genuinely interested in the program.
The weakness of my application lies in my clinical experience (and, perhaps, my MCAT at 31S). My GPA, 3.72, has been over 3.85 over the past three and a half years, and I have had several great experiences in leadership positions that have helped me grow and learn an incredible amount (tutoring, resident assistant, etc.). After talking to the dean of admissions at my state's medical school, it's clear to me that my clinical experience was lacking. For that reason, I am now working in the emergency department at two local hospitals. I have worked directly with nearly 40 different physicians there as a scribe, creating patient's medical records and observing and assisting the physician.
That said, my consideration of declining an interview stems not only from my interest in medical administration and policy formation (and thus my application to the M.S. program), but also that I might strengthen my application so I have a solid, well-balanced application and a good chance at the schools in which I am interested to train to be a physician.
While it's really hard for me to think that I would decline an interview invite, it seems like the right thing to do to become a better applicant with wider opportunities. Not only that, but for some reason there is a strong push for pre-med students and individuals to get in and out as fast as possible, whereas I seem to like the process just as much... Which, perhaps, indicates to me that I would be comfortable waiting.
Anyway, thanks again for your ideas, everyone! I'm waiting on an email from one of the directors of the M.S. program, so we'll see what he says before I make a decision.
Good luck everyone!