Take what I say with a grain of salt, because I am not an expert on the Avios program. But...is your ticket booked with cash or with Avios? If booked with Avios, you'd essentially need to re-issue for a F award, and that depends on QR opening up award F space on the flight, and might affect the pricing of the entire award. QR does allow redemptions for twice the Avios cost (i.e. not normal award space) through its own Avios/Privilege Club program. But if booked as cash, or through BA Exec Club, that wouldn't really be available to you.

If your ticket will require that you have award space to upgrade, IME QR won't open up space for upgrade (miles or cash) to F if there is no one yet booked in the F cabin.