I think the Dubliners recorded it. Probably other people have as well. I don't know if it's got an agreed tune. In a setting where it's be appropriate to sintg it there's a sort of ur-melody that attaches itself to words like these.
It's really more of a monologue with a bellowed chorus line.
The sad thing is that you can't get Plain anymore - it was a porter with a little less body than the Guinness they sell now, which was the next grade up(that's why it's got all those Xs, and it's called Guinness Extra Stout). You could drink more of it without ill effects, they say. But they phased it out before my time. Another blow to the drinkin' man. And the drinkin' woman.
I sometimes wonder if St James Infirmary has anything to do with St James's Gate...