There is a definate connection, and yes there are plenty of us in Australia! I live in Sydney and have brothers and sisters. I have done some study into this line over the years. There was a book published some years ago for a family line 'McKay' and there was a large section of that book about Gaddes' and their line in Australia. Someone has posted large parts of that in this forum if you look through you will see it.
My g-g-gradfather is the William that is from England, and my g-g-g-grandfather is as far back as i have been able to ascertain.
I have a son, named after my father, Max Gaddes, i have a brother also named Max. So the Gaddes name in Australia is healthy and has many years to continue!
me = Richard Gaddes 1972 - father = Max Gaddes 1940 - 1983 grandfather= Richard Gaddes c1900-1980/81? (cant remember the exact year) g-grandfather = Richard Gaddes 1858 - 1907 gg-grandfather = William Gaddes 1832 (England)- 1902 (Aust) ggg-grandfather = Richard Gaddes - no details