Backer board bowing on 24" inch steel studs for rock ledger panel installation
This question is either subjective (based on opinion and personal standards of quality) or is a warranty issue. In either case it's probably off-topic. That said, here are my thoughts. 

Yes, adhering the cementboard sheet to the drywall will add stiffness--probably enough to result in a satisfactory substrate, especially when considering the large size of your stones. However, it may not meet warranty requirements for either the cementboard or the stone. 

All that said, tt would probably be trivial to cut out the majority of the drywall at convenient lines and replace it with half inch plywood. Glue your cementboard to that and be sure you won't have problems.