Consider that the 16-bit ADC values come in as 0.16 format, relative to VREF. (Or 1.15 if signed.)
The numbers inside the computer need not have any units at all. Preferably, they're just more arbitrary data to pass around! You should only ever need one unit conversion step, when outputting the value to display or other* DAC.
*That is, a DAC that's separate from the ADC and its VREF, in which case they probably won't exactly match.
Nothing matters for DSP or FFT, as long as the gain is unity, and you don't cause overflow in intermediate steps (and, you provide enough fractional bits as needed for certain purposes -- integrators with very long time constants, or high order IIR filters, for example -- in which case the extra bits can be local to those sections, and truncated or rounded off elsewhere).
On an M0, 8.24 format is probably as effortlessly good, and easy, as you'd need for most purposes? In other words, take the ADC sample, put it in a (u)int32_t, << 8, math it, then >> 8 when you're done.
Incidentally, the added bits can be meaningful. For example, when accumulating values (such as a in "boxcar" FIR filter), you need ceil(Lg(N)) extra bits to hold N samples added together. Assuming uniform, independent quantization noise, we expect to gain about half as many bits in real measurement accuracy. For N = 256 say, we need 8 additional bits, and 4 of them are meaningful (effectively expanding a 16 bit ADC to 20 bits accuracy).
(Or if subtractive dithering is used, nearly all 8 added bits are meaningful!)
Note that uniform and independent quantization noise is not a good bet, when considering the DNL and INL of real ADCs. You'll get more resolution this way, but not necessarily more accuracy. Ideally, you'd calibrate such a system, and introduce a conversion table or piecewise or polynomial correction curve to get real numbers out. This is... heroic effort compared to the $5 to buy a "24-bit" ADC (which might only be 20 bits real accuracy, but there you have it, eh?), so it's not often used. Just FYI, know your errors and statistics.
Tim