My intuitive answer is yes. Not all musical lyrics are poetry, but some musicians are most definitely poets. Dylan even won the Nobel Prize for literature, no one could possibly argue the unique sensibility and authenticity in the lyrics of Cohen, Lennon, Morrison, Reed, and many others.
Poems exist in a silent space. The problem I have with reading just the lyrics is how not to hear the musical elements in my head, how to separate both integral parts of the song, deconstruct it to be able to analyze the lyrics without the accompanying music.
To answer my question, I was having a dilemma choosing between Joad and Tunnel but will say Tunnel because of the lyrical depth. The intensely personal songs, dealing with self-doubt, failure, and disappointment have the right to be classified as poetry. The roller coaster ride is arguably the best metaphor in his repertoire.