I was going to try, but ironically enough the Linux version is available only to Premium subscribers. If you don't have that, you just get the "use of this device is not enabled for your account" error message when trying to log into Spotify.
Running the Windows version in Wine now. The audio quality is just fine, and it seems to be identical in Windows. Either there was an old bug in older versions of Wine, or the website was just trying to get more people to test the Linux version (and thus get Spotify Premium? I don't know).
In any case, there doesn't seem to be any bug or problem with the audio.