Just adding to this old post, that it is indeed possible. I didn't believe it at first as the Recorder plugin documentation states:
"The Wwise Recorder plug-in effect allows designers to record to an AMB, WAV, or WEM file the sound played within the Wwise authoring tool."
But by defining a name like "Recording.wav" into the Game Output Path, it does record while the game (or eg. Unity Editor) is running, and sounds come through the Recorder plugin!
Perhaps AudioKinetic should update their documentation to be more precise on this matter?