Sorry to be a little bit pedantic, but just because Synge mentions the ballad in a play set in the Aran Islands does not mean that the islanders themselves would have been acquainted with the song. Synge was a fairly cosmoplitan kind of guy and would more likely have heard the song in Dublin.

In his book "The Aran Islands"(1906?) he does talk about, and notes the words of, some songs but not, as far as I recall, any Dublin street ballads.