I think you can definitely do it material-wise. Mainly because the Physics II and Orgo II material on the exam is not nearly as in depth as you need to know it for your classes, and if you do not know it already, you can become familiar with EK or Kaplan, etc. info (that's what those materials are there for...those who have forgotten or never really learned it)
However, that is quite a work load. And unless you feel you can effectively balance it all without letting the grades of those core classes or the MCAT suffer as a result of having too much on your plate, you may want to consider taking it in Aug. or taking it when your class-load is a little more slack. Although a lot of people do it that way and get by just fine, it just adds more stress to an already stressful situation having a lot of other stuff going on. Just my 2 cents. Good luck with whatever you decide! 🙂