Hell no
Most people in Australia are, but I was born in South Australia, the only state which never received convicts. (Actually, I'm sure I've got convict in there somewhere, but...)
Basically, by mums side came over on the First Fleet as Royal Marines + their wives. Hortle and Davies.
My dad's side were farmers who came out from Somerset England, and Lutherans who fled religious opression in Prussia.
Most South Australians refer to themselves as 'Blue-Bloods' but no-one really cares.