Firstly, welcome to the Forum ... there's a fount of knowledge here so I hope you stick around!
BA uses Amadeus, and I therefore suspect [indeed almost guarantee] that any BA Holidays booking (Flight + Hotel, for example) is going to have to be on the same GDS.
I also use Hilton [just expired HHons Gold], on the double-dip for Avios, but I don't think I've ever done that through BA Holidays ... just direct with the Hilton of choice. Our BA Holidays bookings have always been with non-Hilton properties.