Insane. Yes.
I know everyone is different... and every course is different (i.e. my o-chem instructor made perfect sense to me, biochem instructor seemed to be rambling about nothing...) but I think that is a really bad idea.
O-chem isn't that hard with a very good general chemistry foundation, but it is still a lot of work. Biochem is a lot of work, and, for me anyway, was almost entirely new information. When I took biochem (and again, some of it may be the instructor), I had 5 science courses. I got 4 A's and 1 C that term. It was a nightmare. Is biochem required for you? I don't think it was very helpful for the MCAT. Cell bio was moderately helpful, and physiology. Probably any advanced biology class would give you the same preparation.
Next story: I took physics over the summer. It was doable, but I was doing hours of physics homework every night. That said, it would be tough to do two classes like this at the same time.
Finally, the MCAT. I actually didn't spend the three months or whatever people do to study for this. I looked at the material a couple of times in the preceding months, but not much. I buckled down and did a pretty decent amount of studying (cut my work hours back to part time, studied all the rest of the time) for about 2 weeks, and I did well. I had just taken a lot of the courses, which helped - just wanted to give you an idea of how much time it took, in case that helps your planning.