In my time I was the US SME for Upgrade using Avios Trade (UuAT), which is slightly different from UuAs on direct bkgs. I don't think BA.com has been scripted to handle them. BA is very reticent to take over a TA bkg prior to departure, the offline UuAT process was an exception to that.
Yes, tickets do need to be issued before upgrading; for UUaT BA doesn't need the agency to do anything once the tkt is issued, so as long as the fare type qualifies, BA will take over the PNR and send the TA an OSI. Other airlines have their own policies of course, but shouldn't need the permission/involvement of the TA as the ticket belongs to the issuing airline anyway.