Can Average Power of a 3-Phase AC motor be calculated from Mean Current & Voltage RMS from each winding?
Can Average Power of a 3-Phase AC motor be calculated from Mean
  Current &amp; Voltage RMS from each winding?


No it can't because the mean current taken on any phase is zero. That leaves you with just the RMS voltage and this is no indication of power.

If you want to definitively measure power on any AC machine you need to know certain things and these can be: -


RMS volts, RMS current and power factor (for each phase)
Instantaneous voltage and instantanous current over one full cycle of power (per phase)


Without power factor, RMS current and RMS voltage are meaningless. Even if you know the power factor, if the waveform of current is not sinusoidal (as it could easily be in a motor core that shows signs of saturation), then you will get an inaccurate answer.

The most accurate method is multiplying instantaneous values of voltages and current then averaging (or integrating) the result. This is how wattmeters work either analogue or digital. Below is a picture of two scenarios where the relative phase of current is changed: -



Hopefully you can see that if the phase angle of current is different to that of voltage then the average value of power reduces. In this next picture I've multiplied a sinewave voltage by the 3rd harmonic of current (usually present in an AC motor) and the resulting power is zero: -



This means that a harmonically distorted RMS current value cannot be reliably used to measure power because the third harmonic has no power content associated with it. As a side note, if the voltage waveform had a 3rd harmonic present (and the load was resistive) then the 3rd harmonic of the voltage would properly multiply with the third harmonic of resistor current to produce a real power.