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QF do not sell WT+ as a codeshare. You can only buy a QF codeshare ticket in WT, CW or F. Until recently, you could not buy QF in J on BA since their J products were quite different until QF installed the skybeds.
BA used to allow on-board upgrades by paying some large number of pounds. I am not sure if they will permit that with a QF codeshare ticket. However, if they still do on-board paid upgrades, I can't see why they would be concerned if you were on QF or BA ticket.
So the question is whether BA still do on-board paid upgrades?
Just checked BA's web site and this is what they say about paid upgrades:
Paying to upgrade your flight ticket.
If you wish to discuss paying to upgrade your flight ticket, please contact your local British Airways office or travel agent, whichever issued your original travel documents.