I'm currently in the Hunter Post Bac program and when I applied I was volunteering at NYU once a week doing administrative stuff (had been for 6 months or so I think). I also had around 5 or 6 years experience as a massage therapist, which was instrumental in my decision to pursue medicine. So I think talking about that experience in my personal statement probably helped me to get in to the program. I also had a good GPA and was taking science coursework at Hunter (as a non degree) and getting good grades and that certainly helped, too.
The Hunter Postbac program, as you probably know, is competitive so I would say that you should probably start volunteering as soon as you can (if you have not/ are not already). If anything, the experience will (hopefully) broaden your horizons and help with your eventual application to medical school.
My time at Hunter has been very rewarding and I recommend the school highly. That said, what the previous writer wrote about being on top of things is true. Some (maybe many) departments at Hunter are short staffed and under funded so you won't have people holding your hand through every step of the educational process. You have to seek out support and most importantly stay connected with the prehealth office. Finally, you need to make friends that will help you negotiate your postbac experiences, celebrate your successes and commiserate with you when frustration rears its ugly head.
Take a good look through the prehealth website -- it may answer many of your questions. It is also frequently updated.
http://www.hunter.cuny.edu/prehealth