I just ran another test with MusicBee already open when the CD is inserted.
In this scenario, the CD does not start playing. The tracks started to show a second or so before getting the error message. The tracks showed in the main window as Track 01, 02, etc. I clicked on play and the CD started to play. I went to the Now Playing tab and the tracks show as Track 01, 02, etc, there is no artist shown, but the times display correctly.