Don't know about BC. I have booked a FC ticket on QF using OP miles and later went back to find at least one more avialable. The conventional wisdom is that QF allocates only two 'free' FC seats per flight and those are fought over by QF, CO, US, AA etc all after those same two seats. Do a search, perhaps in the QF forum. I do remember a discussion on the number of BC seats allocated.

If you want to see what is available for FC/BC, join the QF ff program on line. It will then let you search for reward availability, although only for 2 passengers at a time.