Broadside examples don't seem to use the expression, and the majority of sets found in tradition don't, either; but it isn't unique to the Copper Family version. Cecilia Costello of Birmingham also had it in her version of the song. As Dave has said, most people who sing it now have learned it at one or more removes from the Coppers, though.

The background of the song is examined in more detail in the Forum, at DTStudy: Come Write Me Down

And at folkinfo.org: Come Write Me Down

There was some discussion of "married by asking" there a little while ago, coming to a vague conclusion on much the same lines as here.