Those classes are pretty much required, but you technically don't have to finish them before you apply.
I took the MCAT to evaluate my "appliability" when I was working, but without Orgo prereq. When it was acceptable in my calculations, I applied, and then finished my Orgo prereqs the Spring before matriculation. I quit my job for the class, because my local JuCo didn't offer night classes. The sticking point for you is being able to do well on MCAT without having taken Bio and Chem.
Obviously, the optimal solution would be to find night classes at a JuCo and then take the MCAT. If night classes are not available and you can learn Bio/Chem on your own very well, take the MCAT and push the prereq as late as possible, so you are unemployed for the last amount of time. If you cannot learn Bio/Chem on your own very well, then you would have to quit your job and take those classes before the MCAT.