I would need to have an idea of the time constant of the A/THR control loop (the control loop seems to be a PID).
I doubt you find that info in any pilot training doc. However, you may have a look at the A330 Maintenance Manual in the appropriate section. Not sure you get the info though.
From my experience (A330 Trent engines), in many occasions, I found the autothrust very sluggish to react to speed variations, in different phases of flight (CRZ, APP).
This is very true on APP with AP off in turbulent conditions (referring to Cayenne incident). Having said that, this is a known fact and it's been documented by Airbus.
If not done already, you may also be interested in Airbus FCOM Bulletin 810/1A (JUN 04) dealing with "Thrust acceleration in A/THR modes". This applies to A320 family but it contains very good info on your query.