You can't just plug an Australian Nintendo Wii into a US outlet and expect it to work. Two major barriers stand in the way:
Wii consoles and game discs are region-locked. An Australian Wii (PAL region) will only play PAL-region discs. US games are NTSC-U/C and will be rejected outright.
Australia uses 230–240V AC; the US uses 120V. Plugging an Australian Wii directly into a US outlet will damage the power supply and potentially fry the console.
Even with region-free mods, online services (Nintendo Wi-Fi Connection, Wii Shop Channel) are discontinued. Some games may exhibit video mode issues (50Hz vs 60Hz) on NTSC TVs.