Are resolution increase and noise reduction from oversampling mutually exclusive?
If you just average multiple samples, you are using a very low quality anti-aliasing low-pass filter which can add a ton of noise. If you then re-quantize after averaging, you add still more noise.  

If you don't (re)quantize after a high quality anti-aliasing low-pass filter (but keep a ton more bit of resolution), then noise could still decrease as per (3).  And if you FFT before your resampling to a lower sample rate, you still get the higher bin resolution of a longer FFT.  So (2) and (3) need not be mutually exclusive.