NO! I'm reading the regulation:
CIVIL AVIATION SAFETY REGULATIONS 1998 - REG 201.003
Commonwealth and CASA not liable in certain cases
(1) Neither the Commonwealth nor CASA is liable in negligence or otherwise for any loss or damage incurred by anyone because of, or arising out of, the design, construction, restoration, repair, maintenance or operation of a limited category aircraft or an experimental aircraft, or any act or omission of CASA done or made in good faith in relation to any of those things.
(2) Neither the Commonwealth nor CASA is liable in negligence or otherwise for any loss or damage incurred by anyone because of, or arising out of, CASA exercising powers to conduct tests under regulation 139.135, or any act or omission of CASA done or made in good faith in relation to those powers.
It seems as though they have so long as the act or omission of CASA IS done or made in good faith. (IS added)
Also in a number cases concerning the operation of ASAO aircraft, CASA has been found to have no liability for negligence.
If the Government was at all concerned about liability in these matters it would not allow VH registered gliders, maintained by unlicenced people to be flown by un-licenced pilots.
As a corollary, isn't it true that motor vehicles today are manufactured by firms to a standard, independently(?) certified by engineers not required to be members of any organisation? Thousands of people are killed and maimed on Australian roads each year and yet no one attaches any liability to the government for its administration of the ADR's.