It very much depends on the encoder/decoder. Intuitively, the uncompressed data matches the assumptions of the encoder perfectly and there is no reason to throw away more information since the fixed bitrate can be met.
However, I seem to remember that ATRAC (the minidisc encoding) was explicitly designed to recompress badly in order to degrade any kind of copying (analog or digital via S/PDIF) in addition to the digital copy protection schemes.
Also, there are obviously some things you do in Audacity ("final"/"optimized") that are not pass through, and also in Adobe-Premiere. Even if you only do video cutting, the audio framing will most likely be disturbed (I doubt that independent audio frames are a clean fraction of video frames), causing an entirely new compression ballgame.
If you have any chance to do that, I'd not let Adobe-Premiere reencode but rather repackage the existing MP3. Alternatively, record in WAV. Or at the very least, do all your processing in WAV and only recompress for the final exported video.