This config puts Emirates as the ground handling if I fly an Emirates aircraft, is it possible to assign DNATA to ground handling but Emirates as the branding for all the cargo containers?
As explained on the manual, and in many threads on the forum, the choice of the GSX operator is NOT driven by the livery of the airplane you are flying. Doing so would be not realistic, because it would cause strange issues, like getting european ground operators in the US in the international terminals, just because the AFCAD might have their codes there. The airplane livery, provided the airplane.cfg DOES have its own atc_parking_codes line, will affect ONLY the livery of the cargo containers.
So, if you override the parking codes in the scenery, setting DNATA to be the ground operator, your containers will be Emirates, but ONLY if the airplane developer set the atc_parking_codes to be UAE in the airplane.cfg file, otherwise they take the livery of the ground operator instead.