Certainly not fully automated, however, like most things regarding the B777 there is still a high degree of automation.
When Phil Condit was leader of the 777 design team he said: "the pilot must be able to control the aircraft with his feet on the the floor, not with the rudder pedals - no rudder application should be neccessary, and he can maintain stability with just the yoke."
To achieve this the aircraft has a wheel-rudder cross-tie and a Thrust Assymetry Compensator (TAC). The wheel-rudder cross-tie moves the rudder (up to 8 degrees of deflection) in response to control wheel inputs. The TAC on the other hand, applies up to 10degrees of rudder deflection when the thrust from one engine exceeds the other by 10 percent.