SYD Intl probably won't accept checked luggage until several hours before flight, and staff are normally reluctant to 'open' flights that aren't already open (if hand luggage only). The F check-in does have a lot more flexibility, but even then they may not like doing it.
There's nothing stopping karens from trying to check-in (most likely denied). dropping bag off at Left Luggage (downstairs in Intl terminal near McDonalds), heading to T3 and using the QP there. With some blagging, use of the Qantas International transfers bus could be possible, otherwise it's ~$5 via bus each way (or train - but I think you have to buy the ticket at the counter for the $5 transfer)