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!
I am taking it in April with Bio II, Orgo II and a bunch of other GE's... not too bad, although I have completely neglected my school work for this beast... it's doable though, just gotta schedule and most importantly, follow that schedule religiously.
I'm a post-bac and I'm doing it. Just remain focussed and budget your time. I study for the MCAT about 6 hours/day and study for my classes about 2 hours/day alternating days. My classes are complimentary to the MCAT work so I'm not super worried about "reviewing" new material. Just know that you need to give up partying or major travel this semster to do it, and warn your friends, so you'll still have them when you're done (if they're true friends, they'll understand).