The consensus from other threads has been no, as it's not a typical booking with a PNR that you can manage. Could perhaps try asking to add it at check-in, as presumably some kind of record is created in Amadeus eventually so boarding passes can be issued, but even if they take it, it may not make any difference depending on the terms of the charter agreement, where the overall product agreed to can be same, better, or worse than regular BA service.