Had a quick look through the manuals and yes you require the ADP to provide enough power to drive the HDG. The RAT function is centre flying control pressure only.
The HDG is solely for AC bus failures and will produce 5 KVa. It is an electrical back up only.
The HDG can be driven by the electric pumps when testing on the ground so theoretically the rat could produce enough power to run it but Boeing installed a check valve so it can't.
Dual Engine failure you are on battery buses only, rat or windmilling for hydraulics.
Without looking in the MEL I presume with a u/s ADP it will drop you to non-ETOPS. Haven't got one to hand to check.