If you purchase the Australian version of Saints Row 4, you won't be able to play online with friends using the international edition.
The confirmation comes from the game's official Facebook page:
"While we are very proud of all our different missions, we do feel that Saints Row IV on the whole remains largely the same without this single optional mission, and we also feel that you deserve to know what you are getting in Australia," a post announced.
"Due to the changes we were forced to make, this version is different than the version rated by rating boards like the ESRB, USK, and PEGI, which is why it will be incompatible with those versions in co-op."
The post notes that Volition and Deep Silver "would have very much preferred" to give Australia the same version as everywhere else.
Interestingly, New Zealand will receive the International edition.
As many commenters have noted, only the Xbox 360 version of Saints Row 4 will be region locked, so players could technically import it on PC or PlayStation 3 from New Zealand or, indeed, anywhere they like - but importing Refused Classification material has legal consequences and is certainly not recommended.