Actually, if driven by a very low resistance like a saturated MOSFET, that measure of RMS voltage -will- be accurate.
However, the power will not be. And using an RC lowpass filter will only give you the average/RMS voltage for a square wave, not the power.
For the power, you need to know the current. If it is a resistive load, it is a doddle as you now the voltage and so the power is simply V^2 / R.
If it is a capacitive or inductive load, you are going to need a series current sense resistor and a fast ADC to capture a lot of samples during a cycle.