Is automatic switching of audio stereo balance while cutting between camera angles possible?
Is it possible?  Sure, just setup each source clip as a sequence that has the audio feed you want for that shot and leave the tracks linked so that you cut between both video and audio.  

Is it advisable?  Probably not.  People are far less used to changing of the audio scene they are watching.  Video creates kind of a disconnect between the scene we are seeing and the audio we are hearing and it may be a bit jarring and break continuity to try radically changing the audio image every time you make a cut.

Go ahead and try it, I may be incorrect on how it will come off since I have not personally tried it, but in my experience with both video and audio, it doesn't seem like it will work well.