Does recording desktop audio reduce quality?
Audacity would grab the digital data for recording in this case and since it uses a lossless format for recording you would not lose any information. I don't know about OBS but it would be surprising if they do things differently.

There will be a very slight loss of quality with 320 kbps mp3s. I doubt any human would hear a difference, though. This may become noticable at some point if you keep re-encoding the file again and again, for example for editing the audio later. If you use a low quality source, say 128 kbps mp3, the degradation will be much more pronounced.