I think its the Maharba/dnata staff that leads the person right from the plane, right through arr process, ie, passport control etc, to the plaza where all the greenery is, at SYD T1.
Would be worth it, for a short turnaround time, if SFO777 finds him/herself ineligible for the int - int transfer. for what ever reason.
For a 6 hr tranisit, then, yes, I would have said, forego for the "VIP" service", but for a 3 hr turnaorund time, maybe its worth it.
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I did meant to use the int - int transfer, when I did BNE - SYD - ADL (dom pax on an int flight) a few year ago, when QFi still flew into and out of ADL, but then they stopped doing the QF81 ADL stop over.
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Take a look at Youtube, not me, (1toyminion), int - int at SYD, she had an NZ passport, so easier if you do, SFO777, have a look see anyway, as to what to expect.
About 37secs in would be the one info sec you need.
As I mentioned, I haven't done it myself, so can't say if it will succeed in your case.
Best of luck anyroad.