So far as I can tell, for the Aussies, its a pointless question. Many Aussie units didn't even get P37 webbing or Khaki drill uniform until they had been in the desert for a couple of weeks. I doubt they will have blanco'd in the desert where water is rationed. My guess is that when shipped back to defend the approaches to Australia they will not have even heard of Blanco. In the Jungle they eventually dyed their uniforms green, its possible that they may have dyed webbing at the same time. Blanco would not work well in jungle conditions so would be pointless.
Not the case I'm afraid - Australians were into Blanco, home brewed too. (An Australians didn't just fight in deserts 
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Have a butchers: http://www.blancoandbull.com/blanco-history/
They fought in Greece, Crete and then moved to the desert mainly in WW1 webbing, which they may well have blanco'd the **** out of on the ship over, just for something to do.
By the time they got P37 webbing they were in the desert and water would have been rationed. Many were issued P37 webbing literally on the docks at Tobruk along with Khaki drill uniforms. Others spent 2 weeks or more in WW1 woolen uniforms and gear in the desert.
After Pearl Harbour almost all Aussies went home to fight the Japanese.
Given that to remove blanco, you wash in warm water. I would be surprised if Blanco lasted long in jungle conditions. If they had green dye for their uniforms, surely they would have tried dyeing the webbing too? They were almost certainly not given green blanco very quickly as the troops had to dye their uniforms themselves to start with and then uniforms were dyed on the ships delivering them.
Photo's indicate that White Blanco was definitely used for parade gear and green webbing was evident once the uniforms were green but there is no info I can find indicating that green blanco was used or not used. Khaki was definitely available and would probably have been used in Malaya and Singapore.
