Assume that an MP3 decoder is used that is broken.
To make the MP3 data audible, the decoder does its job and turns the MP3 stream into a PCM stream. The PCM stream can either be directly fed to the soundcard to be turned into an analog signal (or whatever the soundcard is set to do), or it can be dropped into a WAV (or onto a CD, also in PCM).
The WAV would, in this case, sound the same as the the MP3. Where you could hypothetically end up with a difference is if a different MP3 decoder is used for playback than is used to convert to CD.
But it really shouldn't happen that you get a broken decoder. Other considerations are if you have a plain burning program do your MP3 -> WAV (PCM) -> CD job, versus having something like Foobar2000 (and its more advanced settings) do your playback.
Back to the original question, when an MP3 is decoded, to be sent to either the sound card or to a CD, it should be a purely digital series of steps.
CD Audio & MP3 @ Wikipedia:
http://en.wikipedia.org/wiki/CD_Digital_Audiohttp://en.wikipedia.org/wiki/Mp3EDIT - Added some Wikipedia links to the end.