A couple of issues here:
One of the main criteria for acceptance into medical school is undergraduate GPA (uGPA). A graduate degree or graduate work does not offset or change your uGPA. The special masters programs (SMPs) such as Georgetown's do allow you to take many of the same classes as the (Georgetown) medical students but you have to perform well in these programs. To turn in a mediocre performance can tank your application to any medical school.
SMPs are also very expensive and thus add to your debt load. You need to keep this in mind especially if your SMP is located in a city where the cost of living is high. You will not be able to work and you will have to be ready to devote your full attention to your studies. That being said, a strong performance in an SMP can make your application more competitive for medical school but they won't raise your uGPA (in other words, at schools that screen by uGPA, you will still be out of options).
Post bacc work will raise your uGPA but the process is long and is even longer if you have loads of hours and a low uGPA. If you are ready for the long haul and have a source of income/finance, this may be a good option for you. It can also help upgrade you knowledge base for the MCAT which you would likely need to retake if you spend more than 3 years doing post-bacc work. The best case scenario is a strong performance in a post bacc with automatic linkage into a particular medical school. Again, do be prepared to work very, very hard in one of these programs.
Other graduate degrees such as MPH (Masters of Public Health), MBA (Master of Business Administration and MS (Master of Science) in any field do not raise your uGPA or make you that much more competitive for medical school. These degrees are a means to an end within themselves and are useful if you want to obtain these types of masters degrees. You also need to complete them before matriculation into medical school thus, many medical schools will not interview you unless you are either finished or very close to finishing. Again, these degrees are not going to make you more competitive for medical school if you were not competitive before undertaking these degrees.
You also need to be aware that grade inflation is rampant in graduate school which means that your grades need to be very high. You need a minimum 3.0 average to stay in graduate school and you need to be well above 3.5 to be considered a strong performer. In graduate school, it is assumed that you are studying subject matter that you love and have strong interest in and thus you need to do very well. In the end, your graduate work (outside of an SMP) will be weighted about the same as an extracurricular activity.
