No it's not airworthy, although the guy who was restoring it was attempting to do the work to an equivalent sort of standard. Unfortunately it would face enormous difficulties in being made airworthy because as far as I know there isn't any accompanying paperwork, traceability of parts, etc, etc.
Bevan666 is quite right. There is always something more to these projects than meets the eye (from personal experience) and they can get awfully complex.
As for the RAAF Museum, they have more than enough on their plate. They have almost finished a superb restoration of a Walrus, and will soon be attacking the restoration of the only surviving Mosquito in the world to have seen operational service during WW2 (and with the RAAF at that). As always, they do this undermanned, underresourced and underfunded. The RAAF flew Sptifires, so I'm sure they'd love to have a Spitfire on display, but I'd be interested to know if, how and under what terms the owner has approached them.
I know for a fact that the RAAF Museum has been taken for a big ride by vintage aircraft restorers, dealers and owners before (on more than one occasion).