I've looked pretty hard, but I have no direct evidence of local manufacture. However if a local firm of repute (like Bennett & Wood, one of the best known cycle/motor houses in Sydney for 50+ years) say that their bike is "Manufactured in Australia" there's every chance they are not lying. Simply not worth making something like this up if it isn't (largely) true.
There are comments in the 1939 press like, "... an unusually large proportion of the Acme motorcycle has been locally built" and "In appearance, this newcomer, with its Australian-built frame, is "easy" to look at."
It wouldn't surprise me if the frame was locally built, and maybe guards, tank, spokes, rims, handlebars, levers,... leaving the engine/gear unit, fork, saddle, lights... imported from the UK, then the whole thing assembled here? More or less.
We mustn't forget that there was active industry in Australia at the time. Beginning around 1940, for example, Tilbrook in Adelaide made a wide selection of parts and accessories for motorcycles.
But yes, it would be fun to know exactly what went on!
Leon