Whether for all zero order reactions rate is independent of concentration of reactants
I think the issue is not that you can't define overall order, but that it isn't a meaningful quantity. This gets at the point that Zhe was making that while we can define the total order of a reaction as the sum of the exponents, it doesn't tell us anything about how the reaction occurs. 

Your question gives a very good example of why it isn't a useful quantity: you might expect a zeroth order reaction to have no dependence on the concentration of reactants, but your reaction clearly depends on the concentration of $\ce{A} \text{ and } \ce{B}$, so the total reaction order isn't actually telling us anything about the kinetics of the reaction. 

If the order of a particular reactant is zero however, you can say that its concentration won't affect the rate of reaction (within certain limits, as no reaction can be entirely independent of the concentration of an involved reactant).