Yes, that is a different twist to the usual story. There are a number of broadside editions at the Bodleian Library, with some variation between them; most have a chorus and the earliest dated examples are of the first part of the nineteenth century:

Wild Rover

It was also printed in American songsters of the mid C19, and seems to have been found in tradition mainly in England and Australia, but also in Canada, the USA, Scotland and Ireland. Number 1173 in the Roud Folk Song Index. It has been suggested that it may have been based on The Green Bed; I don't know about that, but it's certainly the case that there were a good few songs made using the same basic motifs.