Yes, but those cannot be requested at airport check-in.
Rather, they're an additional option to the standard international upgrade request, which has to be registered >24 hours before departure.

​​​​​​https://www.qantas.com/fflyer/dyn/fl...pgrade-rewards
​​​​​​You can request an international Classic Upgrade Reward up until 24 hours before your flight leaves on eligible paid and confirmed tickets and on Economy and Premium Economy Classic Flight Rewards on flights operated by Qantas...

International Classic Upgrade Rewards up to the gate

Qantas is committed to providing international Classic Upgrade Rewards wherever we can. Upgrades may become available at the last minute due to cancellations, no-shows or missed connections. To increase your chances of an upgrade your request can now be further considered at the airport. To be eligible simply select 'upgrade at the airport' when you register for a Classic Upgrade Reward.