Although the answer is yes, you will not be able to play online. Streetpass will still work, but anything involving online interaction will not. This includes online play, Spotpass and patching. To get your patch, you can't do it from the EU eshop directly. Instead, you need to download the .cia files for the US version and install them via devmenu or BigBlueMenu like DLCs.
The reason being with an Australian 3DS, you can only accept the online agreement for the European region. Try get the EU version of game if you want to play online. This applies to both ROMs and retail cartridges.
I myself have a New Zealand 3DS in the same European region.