I think so. BA sold the stake in Galileo yonks ago, too, so there's no conflict in any of this.

I think that "works with Amadeus" may possibly give rise to a slight confusion between two different things. If I've got this right, it's a bit like this.

Amadeus hosts BA reservations. So all of BA's own reservations records etc. live on Amadeus systems. This side of reservations used to be hosted on BA's own inhouse system, affectionately known as Babs (British Airways Booking System, IIRC). She was a venerable old soul, having been around almost since the days that computers still had glowing valves.

Amadeus, Galileo, Sabre, etc. also supply distribution channels to the outside world. So a TA can use his Sabre machine to get information on BA flights, fares, etc. BA supplies this information to Sabre, and Sabre also has direct communication to BA's own reservation system to get real-time information on availability etc. (That used to involve talking to Babs, but now involves talking to Amadeus.)

So this is why a TA using any of the big systems can book BA flights. He will access the information through his own Sabre, or Amadeus, or whatever system. He will make a booking record in Sabre/Amadeus/whatever he's got. That's the TA's booking record. But to make the booking, Sabre/Amadeus/whatever will be talking to BA res (hosted on Amadeus) to find out whether there's availability, and getting BA res to make a booking record for the passenger in its own records and to book him on to the relevant flight.

If an Amadeus TA books a mixed BA and AA itinerary, then things can work like this. Amadeus will be asking BA and AA separately for availability. The TA will create a booking record for the entire trip in Amadeus. But each of BA (in Amadeus) and AA (in Sabre) will also create their own airline booking record as well as booking the passenger on to the flight. So the TA's record will have both the BA and AA flights with all the relevant data. But if you talk to BA res or AA res separately, they may only be able to see their own airline's flights, because they are looking at their own airline's records and not at the TA's.

Of course, if things work well, each airline may get information sectors booked showing the other flights so that they both know about the whole itinerary.

One of the joys of flying mixed BA/QF sectors is that because they're both in Amadeus, the integration is very close and it really is almost like flying on a single airline.