I doubt it. Australia has an implied freedom of political communication (per the Lange and Coleman v Power cases). This law is on shaky legal ground already. Blocking entire sites will make it more likely that the law will be struck down.

It would also be more politically risky.

No doubt they could try - it's technically possible - but I think they wouldn't.

I agree that the fact that this law could be abused in such a way is a compelling objection to it.