Airbus FBW is a path stable rather than a speed stable airplane, as conventional airplanes are. This is achieved by a C* pitch control law, which achieves and keeps a target value of g load (blended with pitch rate). Boeing FBW is very similar but it has added a speed maintaining element, and it is referred to as C*U law. So, Boeing are still speed stable airplanes.
It is important to understand that stability, and the tendency of an airplane to maintain angle of attack, or airspeed or whatever (flight path in the case of the bus) is just that: a tendency.
Therefore, as a result of a gust, updraft or downdraft, the airplane can end up in a slight climb or descent. It can¡t be predicted. It will depend on the gust, on how many, how quick and how intense they are, how long they last and in what sense they go.
The pitch normal law of an airbus is not like an ALT HOLD mode of an AP. It will resist to flight path change, but this does not mean that it will succeed in doing so. It doesn't have to. Flight path will change. All we need is that it resists to change. That's enough. That allows us to easily fly the airplane, just like "normal" longitudinal stability helps in conventional airplanes.
If you fly level and an updraft hits you, the airplane will pitch down (pretty conventional right?) But it is likely that some height is gained. Nothing in the control law makes it recover that, nor even to assume V/S zero. It tries to keep the flight path constant. But… Which flight path? As it changes, the reference to be maintained changes, too. Therefore, if after the upset the airplane it in a shallow climb, that is then the new flight path. If the pitch down reaction was a little "late" and "excessive" this may put the airplane descending, but not to recover an altitude.
If you understand this you will fly the FBW better in gusts. All you have to do is to let the airplane resist for a sec before you make inputs to put her the way you want. If you do it simultaneously you will start the "dance".