My experience, albeit 2 years ago, on a SYD to AKL flight in similar circumstances, was that it caused delay at the gate. When they scanned my boarding pass I was pulled out of the line and they did some sort of authentication of our passports prior to boarding. My 2 travelling companions had the same issues.
As a result I am not sure that skipping the check in counter gave us much advantage, nor the black looks and reminder to go to the check in counter next time.
Things may have changed in2 years ...
Anytime you do OLCI the system will enter a comment "check passports & visas".
If you have checked in luggage, when the CSA goes to print bag tags this comment will popup & need to be cleared prior to bag tags printing out so it's sorted at checkin.
If you have done OLCI & only have carry on just see a ground staff member prior to boarding & say "hi there could you reprint my boarding pass as I checked in online with no bags".
When the CSA reprints the boarding pass the "check passports & visas" comment will appear & can be deleted. They will need to check your passports of course to check you have the valid documentation to enter the US.
As the gate agent will be signed into the boarding application so they may opt to view the 'ineligible to board' list & they can delete the "check passports & visas" comments there without the need to reprint boarding passes.
As not all lounge staff have done boarding of flights they may not be aware of the second method so I think it's just easier to ask for a boarding pass reprint if you have lounge access.
When you have multiple QF flights the comment will only appear against the first flight so for eg CBR/SYD/LAX you only need to deal with this in CBR not SYD as well.