@panzrwagn factor 10. at 24 bit so ~16M steps, loud at level 10M, 10x less at level 1M.
The term "data" is not restricted to digital realm. A vinyl record contains data. Analog signal contains data/information. Whether volume control is carried out in digital or analog domain, it reduces the signal/data. Basic information theory.
Definition of resolution is the ability to transmit fine-scale information. So you could record the speaker and compare the recording to the original data stream. The difference in information content is the loss of resolution. With speakers being sonically the most variable component, variability = low fidelity (true to the source), it is clearly having the greatest effect on sound reproduction (except room maybe). As nothing good can be added, it can only loose information, and typically loss happens at the fine grained end, so loss of resolution. Really not rocket science.
Re noise floor, yes, correct mathematically, irrelevant on a practical normal listening level. You need to learn to figure out what is relevant, put things into perspective.
If your regular listening is at 85–90 dB, I pity your ears, or what's left of them.
@everhard Re using/bypassing digital/analog volume, you can easily check whether you can hear a difference by comparing the two volume controls. In a reasonable middle ground (say within 20–80% of digital volume), I would be surprised if you can hear anything.
In theory, you could even go from digital device with volume control straight to power amp (start at low volume) and check effect of preamp on sound.