This is a great point to raise, so I wanted to learn a little more about it and came across this writing from 1896 about the topic of British convicts: http://www.jstor.org/stable/1833611?seq=1#page_scan_tab_contents
With some insight from that, to your question, I would say yes, those countries would have existed. It seemed Britain was in the habit of sending people from their empire whom they found undesirable to the far reaches of their empire, and as you mention for a period before the American Revolution.
Prisoners from their wars were sent (Irish, Scottish), political prisoners, felons, and undesirable citizens were all at some point sent away to a colony (north american, west indies, australia). Interestingly, the American colonies each had a way of handling this practice, and most colonies actively moved against it. For example, Pennsylvania, as mentioned in that article:
“But Pennsylvanians were from early days opposed to receiving convicts. In I722, May 5, their assembly passed an act for imposing a duty on “persons guilty of heinous crimes, and imported into the province as servants or otherwise.” They passed another in I729.”
Massachusetts would levy fines on ship owners whom brought in unsavory characters whom were not documented with purpose. This too appears to be another underlying cause of the revolution, where the colonial preferences were ignored by the King. Being this practice started in the 1600s, I would imagine many of the areas touched by British colonization (in several forms) would have evolved as they have. Had the British not colonized I still think most would exist in some form today, though likely at a different scale.