Nope. There are other apps for that. What the Refills App tracks is when your medications are up for re-order/refill. It offers an easy at-a-glance review of due dates on multiple medications.
Refills gives you advanced warning on when you need to refill your meds, and gives you an easy way to call your doctor or pharmacy directly from within the app on your iPhone.
People were growing increasingly tired of my complaining that there wasn't an app that would easily track medication renewals. I figured I'd better just get it done or risk being mocked for life (or beaten up).