That link works. I'm not sure, however, that the tune much resembles "Garryowen"!
Rex, I've noted several newspaper refs. to "Garryowen" (or "Garione") in U.S. before the Civil War. I don't have the texts handy, but here are the dates and the states:
NY 1818, 1826, 1836, 1843
DC 1823
SC 1823, 1828
VT 1827
TN 1838
NH 1841
MA 1844
ME 1850
Mention of the playing of such tunes by title was rare (no "feature sections" in the press). This many suggests that "Garryowen" was well known in the U.S. by 1861 in Irish-American communities on the East Coast.