The speed autothrust is trying to attain is always more than V.a.prot. If the thrust were sufficient, you wouldn't be at V.a.prot in the first place. Autothrust doesn't forget about it's target speed just because you are so slow that the protection is pushing the nose down.
This protection is completely independent of the autothrust. Remember the autothrust has no control of pitch.
The inputs into the ELACs are: (from the FCOM Flight Control Schematics)
- ON/OFF switches
- Sidesticks
- FMGCs
- ADIRUs
- SFCCs
- LGCIUs
- Hydraulic Pressure
- RAs (roll only)
- Accelerometer (Pitch only - not sure what this is)
- Rudder Pedals (Yaw only)