how to compute the average power from AC generator
As an alternative, can I use non-rectified AC voltage and the current
  to compute the average power?


If you want an accurate number for power this is the only sensible way to do it because any other method will be only accurate if the voltage supply is sinusoidal and the current drawn has no harmonics. 

Take high-speed simultaneous samples of voltage and current waveforms. Multiply i and v samples. Average over a period to suit you (best and most accurate if taken over integer numbers of AC cycles). This is proper average power.

If the current or voltage has harmonics then you need to sample sufficiently high enough to be able to ignore aliasing effects.

EDIT showing voltage and current waveforms multiplied together. V is blue, I is red and magenta is power: -