Absolutely correct, meself.

I know because when I used to discuss the lyrics with undergraduates I'd always point that out.

Jack, "The Corbie and Craw" [sic] appears on p. 403 of "The Book of Scottish Song" (Glasgow: Blackie & Son, 1844), attributed to "Alex. Carlile."

The text is nearly identical, but the "craw" is male. Spelling and dialect are slightly more English-y.