Not necessarily. Challenges are based on points, not miles. Lower fares earn 0.5 points/mile, so SYD-LAX-SYD would net just under 7,500 points - well below the 10,000 you need. To do it in one round trip, you'd have to either continue on to the U.S. east coast or route via NRT.

And that's if you book an AA flight number. If you book as QF, which is often cheaper, the lower fare classes only earn half the actual distance in AA miles - and then half of that in points.

In other words, be prepared to shell out more than the absolute minimum if you plan on achieving AA Platinum status this way.