Yes. Most Australian native mammals are marsupials and we have a large group of different tree dwelling marsupials that fill a similar ecological niche in Australia, to the one squirrels occupy in North America. Because the only marsupials early Australian naturalists were aware of from their education were the American opossums, that name was applied to them here - and it's since been shortened down to just plain possum.
There's a lot of different species and one of the habits of those in suburban areas is to move in and occupy the roofspaces of houses - including in this case, the Prime Minister's official residence.