Is ATC allowed to accept an IFR position report from a VFR pilot and use that for separation purposes?
Why is it an IFR position report? What differentiates an IFR position report from a VFR one? A PPL with CTA endorsement needs to be able to identify and report where they are. A PPL without CTA endorsement needs to be able to identify and avoid CTA. A PPL with a NVFR needs to be able to navigate by navaids or GPS. A night VMC flight requires some "IFR equipment".
Where does this assumption that the VFR is blundering along without knowing where he is come from? Your question is unanswerable because it's based on an incorrect premise.
To answer your hypothetical.
a Night VMC pilot without IFR equipment or rating is at about 15 nm north of Hobart at about 5000' . He could be inbound or outbound or simply crossing the airspace.
How does ATC in the Melbourne Centre provide a class C separation service to an IFR airline aircraft , also to the north , either inbound and outbound ,if the airline aircraft is going to be at about 5000' at 15 nm at the same time?
Firstly, but facetiously, your VFR never got to 15nm north of Hobart at 5000' without a clearance. Lets say he's inbound and 25nm north at 5000' (and has calcuated a LSALT that avoids Mt Hobbs and has put in a flight plan).
VFR: Melbourne Centre, Victor Foxtrot Romeo is 25 miles GPS north of Hobart on the 000 radial at 5000'. Request clearance.
ML: Victor Foxtrot Romeo, Melbourne Centre. Clearance not available. Remain OCTA.
VFR: Remain OCTA, Victor Foxtrot Romeo.
There - impossible achieved - if ML Centre isn't busy I'm sure he'll also issue an expect onwards clearance time. Now, if traffic permits and our VFR guy just wants to transit say Strahan to Maira Island at 5000' and there is a northerly blowing.
ML: VFR, cleared Mangalore to Prossers Sugarloaf at 5000, remain outside 20DME Hobart.
ML: IFR, cleared to Hobart, descend to 6000' not below the DME steps, report 15DME Hobart.
IFR: 14DME Hobart.
ML: Descend to 4000' not below the DME steps, cleared VOR-Y runway 30.
There. Impossible achieved AGAIN and TWO aircraft in Class C at the SAME TIME without radar. Quick - ring the FAA and ask them how they process IFR movements into remote class E aerodromes without radar (hint - one in/one out - and IFRs are actively encouraged to depart VFR into G and try and pick-up a clearance - like we are in D)?
This is all distinct from the MLAT red-herring which again you are confusing the issue with. If ASA paid for MLAT coverage to TRA standard to ground level at HB and LT and didn't get it then that's a project management issue, not an operational one and I'd be as unhappy as you appear to be.
You forget that other airports in Australia work in similar ways. TW operates Class C without radar. AY operates Class C without radar etc etc. Whether the man in the tower or at centre operates that airspace, neither of them can see it and so it's procedural - day,night, VMC, IMC etc.
UTR
PS I apologise for the male-ification of all this - it's easier to type....