I would say at least the fundamentals of organic chemistry are necessary for an understanding of biochem. For example, how are you going to understand what an aldolase is if you haven't learned the basics of the structure in Organic? Gen. chem as well is important. Not everything, mind you, but there are many principles which you would simply be lost without. BioCHEMISTRY, is meant to be taken after a year of gen. chem, and at least Org. 1, though there are a few things in Org. II which will help.
There are several examples I could advance, however the best method to demonstrate why shortcutting the system is erroneous is to understand the reverse thinking.
Example:
As a practicing physician, you're deciding on appropriate treatment for a specific glycogen storage disorder. The foundation for for understanding the molecular basis of that disorder came from biochem. Understanding the structural organic rearrangements involved in glycogen formation required Organic chemistry. Understanding the thermodynamics involved required some basic general chemistry. Being able to calculate a therapeutic drug regimen requires some basic math skills. Being able to write the orders involved learing the skill in 1st grade. Being able to talk involved learning at age 1, the art of blowing air over your vocal cords, etc. etc.
Quit trying to shortcut. You'd be pretty lost if you had biochem, etc. and skipped learning to write
The lesson to be learned is that no matter how seemingly worthless the class at the time, your older and wiser self soon sees reason behind the insanity. This for biochem, organic, Eng. comp I, sociology, botany, and even that damn Oklahoma Flora class I had to take (not much, but it did help me get fairly proficient at pronouncing Latin. Ok, it's not much, but in anatomy lab, it helps. )
Were you taught clinical medicine without sufficient didactic work, you would in essence be a technician. (i.e. - someone highly skilled in the procedural portion of a profession, however, somewhat lacking in theoretical foundation in order that appropriate change or advancements may be made).
So sit back, take some breaths, and take the classes in the order they were meant to be taken. Many much more educated than yourself obviously think they're important.