I heard this from a recording by Rayna Gellert and Susie Goehring, and I swear that I can sing the Yeats song along to it. Obviously the bluegrass arrangement with fiddle makes it sound different, but to me they are very similar tunes.

I may have come upon a theory about the words. If Wikipedia is to be believed(!) Yeats wrote his poem based on some badly remembered words. It seems Willow Garden - otherwise known as Rose Connally - pre-dates Sally Gardens by some time, so maybe that was the song he was mis-remembering. Doesn't explain the similarity in the tunes though.