Only in so far as the moment a monarch decides to exert any unwelcome authority will be the moment they get deposed. Our monarch performs a ceremonial role as figure-head only.
You might call the independent board "Parliament".
You might call the independent board "Parliament".
How do you know they will get deposed, you are talking about hypothetical situations.
(Corruption of government starts with its secrets, and Australia has .. many .. that would startle its citizens into rebellion, which is what the political system of Australia is truly designed to police, not serve..)