Noise & benefits from reducing pic size from 16mg to 8mg via menu before shot taken..

Say (for example), a P310, has 16 megapixels and a small 1/2.3 sensor. (presumably much noise with high ISO). Can I improve results somewhat by using the Menu to reduce pic size to 12 megapixels, or 8, or even 5? Or will a 12 megapixel camera usually take the better picture (the P300, say). Is the same true for a G12 with CCD sensor?

I'm just wondering if reducing pic size in the Menu sort of increases relative sensor size?
Thanks!