"The volitional form + て" means ~だろう/だろうに when used at the end of a sentence, but this doesn't fit there. I googled 群がろうて and got 540 results, but almost all results are this lyrics. The exceptions are just two; 昔から女がスクアーロに群がろうてしても and そんな奴らがどれだけ群がろうて――無駄だ. The former one is obviously a typo of 群がろうとしても, and the latter is also a typo of 群がろうとて, i.e., 群がっても/群がったとしても (this ~う is for presumptive). I think it's meant 群がろうとて also in the lyrics (群がろうとして in modern Japanese in this case) from the context. Probably the writer misused it.
As you would realize, the lyrics is written in (pseudo)classical style. や in 踊れや is a sentence final particle (よ in modern Japanese), and や in 肥大や is for question, thus, か in modern Japanese, not just for keeping the rhythm with no meaning.