You definitely used to be able to study for up to 3 months on a tourist visa. Some schools used to use it to target overseas students for PPL's.
They've recently changed the visa types and system and the website no longer mentions it. A call to your local Australian embassy/consulate is in order.
Here's a link to a unofficial website that mentions it, but it might be referring to the old visa types.
Tourist visa to Australia - Information Planet