In CLB mode, autothrust sets THR CLB. That is a fixed thrust mode. The control of the pitch (to maintain airspeed in the climb) is the responsibility of the ELAC, following the guidance of the FDs, which is computed by the FMGS.
So yes, the Athr has no control over pitch.
The question that I am not 100% sure of (and will try out if at my next recurrency sim) is this:
Aircraft in level flight. Reduce thrust to idle, speed reduces, protection engages and nose drops to maintain V.a.prot.
Increase thrust to CLB thrust... but do not touch the stick.
One of two things can happen.
1) Aircraft accelerates quickly, and maintains 1g, essentially maintaining its previous trajectory.
2) Aircraft maintains V.a.prot, but due to the increased thrust, and the fact that I have not disconnected the protection (by using forward stick), aircraft pitches up into a steep climb, still maintaining V.a.prot.
I would have thought that (1) was the obvious option, but now having read more, I am not entirely sure.
"Remember, FMGS = A/THR. A/THR system is part of FMGS." - Touche! But I still don't believe that the ELAC knows or cares about the status of the Athr.
"Ok, so how does ELAC know when to maintain a speed > 140kts and when to maintain a speed = Vprot??? "
The ELAC is only responsible for maintaining airspeed in the following modes:
-High AoA protection
-High speed protection
-SRS
-CLB/OP CLB
-DES/OP DES
So in our case, with AP/FDs off, when we have accelerated out of the high AoA protection (speed > V.a.prot), the ELAC is not maintaining any speed at all. It is just flying straight ahead until we move the stick.