How a FBW airplane responds to a disturbance is a function of how the FBW control system has been designed and what control system mode is active. With autopilot engaged controlling to altitude and heading a disturbance that perturbs the airplane away from either will be met by corrective action from the autopilot to control back to the selected altitude and heading. In a similar manner, if the autopilot is in an approach mode following glide slope and localizer signals the system will control back to the center of both guidance beams if disturbed by a gust.
That same airplane operating with the autopilot turned off, but an "augmented manual flight" control system active will reject disturbances per the system design. Most FBW systems have been designed to provide conventional flying qualities wherein the pilot's pitch command calls for pitch rate, normal acceleration, or a combination of both and possibly some level of positive speed stability. In the roll axis, roll command calls for roll rate. In the yaw axis, pedal input calls for sideslip and may or may not simultaneously command roll rate. With no pilot input in any of the three command axes, the FBW system with autopilot disengaged is typically designed to command 1g/zero pitch rate, zero roll rate, and zero sideslip angle. As result, the response to a disturbance that generates pitch rate, roll rate, and/or sideslip will generally return the airplane to zero pitch rate, zero roll rate, and zero sideslip angle but will not make an attempt to return to the pre-disturbance vertical flight path angle, roll angle, or heading. If part of the FBW system, positive speed stability features may command long term nose up or nose down pitch in response to variation in speed away from a trim point.