RC circuit: is order of resistance and capacitor important?

The two circuits you describe:

are basically the same. For example the change of the current with time when we first connect the battery will be the same. There are some obvious but minor differences, for example in the left circuit when we first connect the battery $V_a$ starts at zero and rises to $V$, while in the right circuit $V_a$ starts at $V$ and falls to zero. Aside from this, when you connect a capacitor and resistor in series it doesn't matter which way round you connect them.