Lonewolf 50
... to better understand recovery or lost capability ... if you had a power loss / or interruption .. then, not only do you need to reset location and direction, you have to establish wings level, nose pitch X, (zero, I assume) to re-establish correct attitude sensing from which the gyro can reference.
That is similar to "recaging" a gyroscopic Attitude Indicator if it has "tumbled" in flight, though from your description, a bit more complex
Regarding in-flight realignment. I'm no expert, but I'd venture to say that on a theoretical level:
As long as you can fly in a reasonably straight line, and can build a GPS trajectory of that line, you can then realign the solid state gyro by applying corrections to whatever the gyro displayed during the straight line.
Additional data needed is airspeed and the airplane's lift polar curve data , which gives the angle of attack for any given airspeed (which affects the indicated pitch angle).
In the roll plane, calibration can be aided by the fact that according to aerodynamics, any bank will induce a turn (assuming no sideslip). The actual turn rate can be calculated from the GPS track. In fact there is a definite relationship between airspeed, turn rate and bank angle, so theoretically it should be possible to calibrate the roll axis even if the plane performs a constant rate turn.
I have no idea of the A330's capabilities in this regard, but e.g. the Garmin 1000 integrated instrument system for GA is capable of in-flight realignment.