Let’s say I have an audio file which stretches the full dynamic range of a 24-bit file (theoretically, I know this scenario is unlikely). If I click amplify and reduce it by 20 dB, then amplify it back by 20 dB, all in a 32-bit float DAW, is there any loss? What if I use effects and plugins on the audio when it is still -20 dB? Thanks.
(Edit: I am asking about a 24-bit file in a 32-bit float DAW.)
IF you are doing this manipulation internally to the DAW (operating at 64-bit) then you will experience NO LOSS AT ALL.
However, if you export the file after gain reduction as a 24-bit file, then you will note that there has been a reduction in the number of bits used. These bits are then not recoverable.
If this is part of the mastering chain, then as part of the output process, you could consider using dither which will give you an improved audible experience when using lower bit resolutions.
Taking 20 dB off a 24-bit audio file leaves you with close to 21-bit resolution (1 bit per 6 dB x 3), which still has a whopping 124 dB dynamic range. Are 21 bits per sample enough? Consider that most recordings are ultimately rendered in a 16-bit distribution format (96 dB dynamic range, theoretical). Most real-world listening environments and playback systems effectively knock another 20-40 dB off that number.
Short answer: no, you'll experience no discernible degradation working with your audio file after shedding 20 dB.
Most DAWs of todays do the processing in higher bit-depth accuracy. Although you should consult each DAW's manual or technical support for this, I believe it is reasonable to consider that the processing happens with at least 32-bit depth.
Even more, the internal representation of the samples is something that also needs to be taken into account. 24-bit PCM data is most often represented in integral (integer) values. The conversion from integral to floating point numbers is not necessarily trivial (and most often than not is not trivial). Even if the DAW developer/manufacturer uses IEEE's standard (even without subnormal numbers taken into account) the representable numbers is way more with floating points than with integers (of 24-bit depth).
Thus, you will most probably not get any noticable degradation of the audio material from attenuation of 20 dB.
Regarding the additional processing you mention, this largely depends on the nature of the applied processing. Most probably, you won't get any degradation in this case either, but this has also to do with the implementation of the processor (VST, TMD, AU, etc. plus the way it was implemented by the developers).
