Intuitively, I'd be inclined to answer yes to [A]. But not to jump to conclusion, maybe there is risk of unwanted interaction between the step down transformer and the voltage stabiliser. (Inrush current?)

If the voltage is low but stable, you can use a step down transformer with other voltage levels to compensate for the undervoltage and omit the voltage stabiliser, e.g. a 220V to 127V transformer. The prerequisite for this is that the voltage is reasonably stable or your equipment will let the smoke out as soon as the voltage rises. [Linked Image]