(to both posts prior)
The Airport would be a Sydney Airport. The airlines may choose this airport over Kingsford Smith due to cost/gate access/curfew/etc. Not because they're tapping into Western Sydney.
Just as Luton, Gatwick & Stanstead are all "London" (even if Luton is well outside London's metro area), just as Newark & Teterboro are effectively New York airports despite being in New Jersey.
It's fanciful (at present, at least) to assume that International tourists arrive in Sydney & will then want to proceed directly to Parramatta & not Sydney CBD. I don't say that with any disrespect to Parramatta of course; but until Parramatta has a world famous Opera House etc, it's just not in the running.
People from the CBD/North/East will definitely visit this airport. If (say) Cathay Pacific only fly out of Badgery's Creek & not Mascot, I can't imagine someone from Chatswood electing to fly Qantas at $200 more per person (for arguments sake) purely because of Airport. If Aerolineas are the only route from Sydney to Buenos Aires, you bet someone from Randwick would trek to Badgery's Creek rather than fly United & have to transit in LAX just to depart Mascot.
I can't imagine any planner (not even the bean counters in NSW treasury) would create a link to this airport that doesn't provide a direct link to Sydney CBD.
Some airlines may initially choose the new airport, assuming passenger facilities (and international passenger facilities, if you are talking international flights) are provided.
But the level of demand that you need to make any rail link worthwhile, let alone an express link to Central, is huge. You are not going to achieve that huge level of demand in the medium term.
Airlines that choose to fly to that airport because of airport charges are not likely to be targeting premium traffic. But it is premium traffic, and lots of it, that you need to be pay for any express CBD link.
Planning for it is fine. Building it upfront is not.
(It will need to be an impressively lengthy train trip from the Sydney CBD to catch an Aerolineas flight to Buenos Aires, as of next week. I'd suggest Qantas (direct) or LAN (via Auckland), with connection in Santiago, are perhaps more practical options. From personal experience QF is better on the way there, LAN on the way back. The QF flight is premium heavy the whole way (LAN only east of Auckland) - it won't be moving from Mascot anytime soon.)