As far as i know GLS (or GBAS) is only certified for CAT I operation. The company i fly for was the first in europe being certified for operational use of GLS, but only CAT I as well. Autoland and automatic rollout was possible, but not approved. We did however do test flights for CAT IIIb/c trials which were extremely successful, however the system is still not approved for more than CAT I.
Sadly we are not GLS capable anymore as we switched from 737NG where GLS was available at no extra cost from the OEM to airbus where only a retrofit at around 250k € per airframe is available, a cost which is simply to high for no real extra capability.