Will Australians be able to build from source, install and connect to the central server (if any)? Or at least build and verify that what comes from the stores is what they built? If not, having the source code doesn't really matter much.

I think it would go a long way in establishing trust if they release the source code, even if you can't perfectly prove that the binaries are built from it. They would have to be outright lying if that wasn't the case.