It's discontinuous.
You have some low noise amplifier. There is a signal. You split it. The result on each side has >=1 bit worse noise floor, probably somewhat worse as we're not using superconductors :P-- as you expect: there is no free lunch.
Now: take one copy and attenuate it 48dB, further degrading its noise floor. Sample both. The attenuated copy is mostly useless, except when the input goes high enough that it would have hard clipped the other ADC.
So the tradeoff is that you lose a small amount of noise floor constantly-- out at the 20th bit, that you probably didn't care about (microphone self-noise is limiting you out there anyways at normal volume levels), in exchange for never clipping.
To turn this into a better ADC generally, you'd need the splitting stage to not hurt the noise floor, but it does.
The reason it's not the same as just lowering the gain so that you won't ever clip is that to get the same dynamic range you'd have to lower it by 48dB and now your ADC doesn't achieve its potential for typical signals. You could lower the gain by 3dB (or whatever the splitting cost you) and get the same results for the low gain signal and a little more headroom, but you would not get the massive headroom increase of this approach.
For this to work one must also have amplifiers with much wider dynamic range and SNR than ADCs, but we do.
The natural output for this approach is a float-- the most natural would be a weird float where instead of an exponent one bit tells you which ADC is in use and represents a factor of 256 or whatever, but in practice these recorders just output 32-bit floats. I haven't looked but I wouldn't be surprised if there were only two exponent values ever used in their output.