Saw something like that at tunearch.org. Needs a careful read. Bold type added:

“Military use of "Garryowen" as a march tune was quite early. The melody was the designated regimental march of the Royal Irish Regiment, organized in 1684 from Irish pikemen and musketeers by the Earl of Granard to fight for King William or Orange in the Williamite Wars (although its adoption may not date from that era).”

We've worked that back to 1798 Limerick, so far. The lyrics seem a little pegged to their times to be all that old. The tune could be another story.