Sometimes codeshare partners share the same bucket of seats and its a matter of both can sell until there are no seats left. Under this model, if there was say 10 business class seats still available on the flight, one codeshare partner (say the operating airline) may be willing to sell all 10 as J and 5 of them a D tickets. At the same time the non-operating partner may sold close to its target sales in business class and may only offering 4 J seats for sale and no more D seats. However, if the operating airline managed to sell 7 of the remaining seats, the non-operating airline will show a reduced available inventory of 3 seats.
Sometimes the codeshare partners have their own individual allocations of seats, and one airline may be sold out while the other still have seats available. In this case, one airline could be sold out in all its business class buckets while the other has seats remaining for sale. It depends on what agreement is in place between the codesharing airlines.
I believe the QF/AA/BA codeshares on the QF-operated trans-Pacific flights follow the first model, while the QF/LA codeshares operated by LA follow the second model.
One way to get an indication as to which model may be used is to look at the available seat maps for each of the codeshare partners. If both show the full seat map for the operating aircraft type, then it is most likely the first model that is in use. If the seat maps show different seats and the sum of the codeshare operators seat maps adds up to a complete map, then that indicates the second model is in use. These seat maps can look strange, while either whole rows or blocks of rows missing from each airline's maps, or one airline showing say ABC DEF and the other airline showing HJK on the same row. In this case they do not even show the other airline's allocation of seats as either being available or allocated - they are just not even included in the seat map. Have a look at the LA and QF codeshares to SCL for an example of these strange looking seat maps.
So the answer to the original question is that it depends on the codeshare agreement between the two (or more) airlines. And the agreements vary and are not public information.
Note that Qantas only allocates waitlisted upgrades within the last 24 hours or so of the flight. So it does not matter what the availability is showing further out than 24 hours. No upgrades are cleared before that time. Also note that they rarely allocate all unsold business class seats for upgrades. They like to keep some available for last minute changes such as for passengers who may have missed a connection to a different flight and need to be slotted onto that flight as a displaced passenger. If they filled all available business class seats with waitlisted upgrades 24 hours before departure, then they would not have the operational flexibility to cope with missed connections etc.
.
