There are a number of audio artifacts in MP3s that are much more noticeable after training. However, many of them become much less discernable with variable compression rates and lower compression (>256kbps). It's possible to train on those artifacts, but I've always avoided it since I don't want the "projectionist effect" of making standard recordings less enjoyable.
This is not the case for many audiophiles. They want to fix all the bugs!