Jamie Raeburn's Lament/Farewell or whatever is pure invention. There never was any such person. The guy who started Greentrax(?) an ex-Edinburgh Policemen went to great trouble to try and trace him through Police and Court records and found absolutely nothing.

Felons convicted by Scottish Courts were rarely if ever transported (Notable exceptions being "politicals", e.g. Thomas Muir). This was due mainly to loss of population in Scotland in the early and mid 18th century. It was a much more common sentence in England and Ireland (Ratio being 5:1 according to the extensive records that exist of those transported initially to Botany Bay and latterly to Tasmania). Convict Transports only sailed from English and Irish Ports (London, Portsmouth, Portland and from Dublin and Cork).