I've had to check in very early in SYD before, though in J. It wasn't possible. I had to use the luggage store for about 7 hours, before checking in.
Serfty- sometimes people have arrive really early, and don't want to lug their bags all over town, but not wait at the airport. I had taken a train from my grandparents house to the city to meet family for lunch, and friends for dinner, before a late flight to NRT. Not having checked out of a hotel, I couldn't leave my bags there, and having taken the train, not a rental car, there was no trunk to leave them in!
OP- you can ask, as you are in F, but they will probably direct you to the luggage store. The cost was reasonable- about $10 for a couple of bags for 5 or 6 hours IIRC.