Yes. MP3 is lossy so if you re-encode the new file to MP3 with Audacity/LAME, you will lose quality. But if you output the cropped file using a lossless codec such as FLAC, the quality should be no worse than the imported MP3.
Some other tools allow you to crop MP3 tracks without re-encoding, such as mp3splt and mp3DirectCut. See How do I split an MP3 file without re-encoding it?