You used to be able to get away with it - until the Oz Government started fining UA for breaking it's traffic restrictions on the MEL-SYD tag of it's flight to/from the west coast of the U.S. UA was permitted by the Oz Government to fly MEL-SYD provided the only passengers carried were those connecting to/from a UA flight to/from the U.S. According to UA sales here in SYD, the restriction also extends to the UA codeshares from Hawaii (on AC) and N.Z. (on NZ). The only connections permitted are those to/from the UA 744 services to/from LAX/SFO. I believe the same restrictions are in place for QF on their LAX-NYC tag so it's probably a bilateral limitation.

Because of the fines, it's now UA MEL/SYD check-in themselves that are denying passengers at the desk if they slip through all the other checks and balances in place and won't allow them to travel on the sector unless they are continuing onwards, or arrived on, UA only. At the start of the crackdown, there was almost a daily parade of denied travellers having to purchase best fare of the day with QF - on day of travel, that usually 'aint cheap!

They also had a blitz on the local travel industry community advising of the restriction and as such the travel agents here are now (or should be) well aware of UA's traffic restrictions and the consequences for the passenger at the airport if the MEL-SYD flight is incorrectly booked.
If making a booking on an agency GDS/CRS for the UA MEL-SYD flight, there is a warning that comes up stating "ONLINE stopover/connecting traffic only" as a further advice for agents.