Hello gums,
If you were asking about ops in the normal range of AoAs, the answer is yes on most current transports.
With the A/THR off, but the AFS in speed mode, the AFS controls speed with elevator. So, if (s)he wants to do it that way, the pilot can adjust VS by changing the thrust manually. The most common scenario might be in a descent at idle thrust, if the a/c is going low on the profile and the pilot doesn't want to reduce the IAS/Mach, but it would work the same in a climb.
if the AFS is in altitude-hold, VS, (or FPA) mode, the pilot would of course be controlling IAS/Mach with thrust. And, if the A/THR was restored, it would use thrust to achieve whatever IAS/Mach the pilot calls for.
Returning to topic, you say:
"It's good for some to realize that you do not have to increase speed/AoA to climb or descend."
I would argue that the only way to initiate an increase in the FPA is to increase
total lift. We are considering a case where the AoA is already at the maximum permitted. In a steady atmosphere - without
briefly increasing the IAS - total lift can only be increased by increasing the vertical component of thrust, and/or reducing the HS downforce.
Re the vertical component of thrust, the high attitude obviously provides some effect in this case.
Re reducing the elevator downforce, the pitch couple with increasing thrust on an aeroplane with under-slung engines means that - bearing in mind that the A320 is not a canard
- the HS downforce has to be reduced to counteract the pitch-couple. So the elevators move down accordingly, which - as I pointed out yesterday - can be seen on the Habsheim DFDR.
Does that make sense?