If I use the “Bass and Treble” function to reduce the bass, and then increase it again (possibly making several adjustments in total), will I end up with (close to) the original sound, or will it be degraded in some way (like making a copy of a copy, only with the frequencies)?
If the track is 32-bit float format, then there is no degradation.
If the track is not 32-bit (if it is 16-bit or 24-bit) then there will be a small amount of degradation, the worst being 16-bit.
The sample format (32-bit float or other) is shown in the track control panel: Audio Tracks - Audacity Manual
and can be change in the track dropdown menu: Audio Track Dropdown Menu - Audacity Manual
The default is 32-bit float.