A bit confusing;
From B737NG FCOM:
Yaw damper operation does not result in rudder pedal
movement. Only main yaw damper inputs are shown on the yaw damper indicator.
The pilot can override either main or standby yaw damper inputs using either the
rudder pedals or trim inputs.
No pedal movement, but you can trim with autopilot and yaw damper engaged.
FB