Yes Arkie, the wearing of the shawl did signify that the girl wearing it was spoken for. Hence the song is really a comedic tale of a young minstrel thinking he's struck lucky, in fact if you take the words literally the shawl is ALL she wears. But the shawl symbolically acts as a protection in the shape of her Father, to protect her virtue. The joke in Ireland is that The Galway Shawl is an old form of birth control, and that you can buy the shawl in packets of three! ;)