No, winRAR and other such "zipping" tools compresses files lossless as good as possible, always having the file back to the exact byte it was before you compressed it.
The file might come out corrupt or something like that in rare occasions, but nothing gets degraded thanks to the compressing mehtod, another great compressor that is IMO better than winRAR is 7zip, compresses its file format 7z better than .rar and can also compress/decompress .rar's and many other formats.
Keep in mind though that an MP3 already is a compressed file and can thus not be much more compressed by such software.