Actually UP noise tends to be highly correlated, so averaging is
not very effective. As you state it has to be white or nearly so to
gain ENOB.
Regards, Dana.
A few years (maybe more than 10 yikes) back i looked at ^^^ this on one of my embedded projects, that used a typical 8b microcontroller (can't actually remember if it were a Pic or an AVR, but one or the other!) and i logged a LOT of data and ran it through some processing, and found that, in that particular application, there was 2 bits of valid extra resolution available.
OK, in that case, i had all sorts of noise sources, from the processor itself, the DC:DC switcher powering the board, 50Hz mains hum, even serial and CAN data buses flipping their bits all over the place in the locality of the ADC. Those wide frequency range noise sources were all hetrodyned together and formed a rough approximation of pure white noise, enough to predictably get those two extra bits anyway.
I'll have to go an find the graphs i produced (must be on one of my back up HD's somewhere)