My great grandfather had a brother who went to Australia. And stayed. No contact with that distant branch of the family. But he went there from the US, not from England on a prison ship. Still ... he was probably a horse thief. Who knows what lurks in the ol' family tree?
I can't prove old Harry was a thief, but the timing is very suspicious. And his arrival here in America corresponds with his "sentence" in Australia being up.
After serving their "sentences" in Australia, IIRC, they weren't alloed back into England, but they could leave Australia.