There is a photo of a No4 being carried in the swamps of New guinea on the cover of, "A Bastard of a Place", by Peter Brune. It is an AustralianWar Memorial photo, AWM 013971. Right there in the foreground is a grim-looking Digger clutching a No4. The photo "description" reads, " Troops of the 2/7th Cavalry make their way through a swamp to forward positions on the Sanananda front".
My own dad, who was a motor-mechanic in an Army Workshop at the time, swore that several individuals were issued No4 rifles. I suspect that the "proper" (No1Mk111(*)) rifles were used at the pointy end (apart from that "stray" at Sanananda), to simplify logistics in the field.
Dad never got much further north than Townsville whilst waiting for "Operation Olympus" to begin. Thus, between fixing busted gun-tractors and Bren Carriers, he and his fellow fitters and mechanics produced all manner of "souvenirs" made from old shell-casings of all sizes, aircraft canopy perspex, fuze-caps from 3.7" AA projectiles, etc. There was so much "once-fired" brass around, some enterprising lad set up a small foundry and was knocking out cast, solid brass models of commonly seen aircraft, like the Lightning and the Hudson. ("I have no live animals or farm-produce in my possession, SAH!")
Any No4 rifles in Oz service were probably diverted there after the fall of Singapore, that garrison no longer needing them.