As you'd hope, Audacity internally uses floating-point math, so your operations truly have lost nothing.
If you specify the file format for 32bit float, yes, for 16 and 24bit PCM, I think no, from past experiments. I don't think the export/import is necessary when Audacity is set for 16 or 24 bit PCM.
Example:
Second track has gone -60dB and +60dB. No export/import, and no dither. Now it has flat tops and stair-steps
Can you tell them apart now?
Sure can, but...
Whose DAC uses 16 bits for volume control?
---
Below, showing the difference between a 16bit source, using 24bit integer volume control, and attenuating/amplifying by 60dB, results in a difference (noise?) between the 16bit input and 24bit output at least 80dB down.
My dac uses 32 bit, don't know if it floats it or not, rather irrelcevant, I think.
Let's see:
"a 32-bit dithered volume control for digital inputs"
Ok, good enough.