Most large aircraft have an integral turn co-ordination function within the yaw damper to minimise the lateral acceleration by applying a small amount of rudder in turning flight
The co-ordination system is generally independent of the AP - a stand alone system, or if part of an integrated flight control system, it would not depend on AP engagement.
In an aircraft with well optimised turn co-ordination and yaw damping there should be no need to use rudder in normal flight. Any manual rudder input could confuse the system, temporarily, or be out of phase, resulting in even more acceleration.
The quality of turn co-ordination relates to the aircraft characteristics, control system (e.g. spoiler for roll), flight conditions, and system fidelity; an ‘optimised compromise’, there may be some transient deviations when rolling, which reduce, to become balanced in a steady turn.
Note; check which parameter the ‘slip/skid’ indicator uses and its scaling, - lateral acceleration?