Series RLC Circuit reduction possible?
In your circuit the differential equation given by KVL is
$$IR_1+\frac{1}{C_1}\int{I}dt+L\frac{dI}{dt}+R_2I+\frac{1}{C_2}\int{I}dt= 0$$
which can be shown to be equal to 
$$I(R_1+R_2)+(\frac{1}{C_1}+\frac{1}{C_2})\int{I}dt+L\frac{dI}{dt}= 0$$
which can be rewritten as:
$$IR+\frac{1}{C}\int{I}dt+L\frac{dI}{dt}= 0$$
where $$R=R_1+R_2$$
is the equivalent series resistance and
$$C=1/C_1+1/C_2$$
is the equivalent series capacitance in the circuit.

So yes, you can rewrite this in this manner and you will see the same differential equations governing the system's current. Thus, this shouldn't pose a problem in your analysis. The only concern I would have is if phase information might be lost when combining the capacitances, but I don't think that it will be.