Indeed the 320/1 autothrust does modulate speed in relation to groundspeed. The PFD displays a Vapp target during approach, so in fact either the autothrust or manual thrust can follow this variable target. It is called Ground Speed MINI(mum)
FCOM says:
GROUND SPEED MINI FUNCTION PRINCIPLE
The purpose of the ground speed mini function is to take advantage of the aircraft inertia, when the wind conditions vary during the approach. It does so by providing the crew with an adequate indicated speed target. When the aircraft flies this indicated speed target, the energy of the aircraft is maintained above a minimum level ensuring standard aerodynamic margins versus stall.
If the A/THR is active in SPEED mode, it will automatically follow the IAS target, ensuring an efficient thrust management during the approach.
The minimum energy level is the energy level the aircraft will have at touch down if it lands at VAPP speed with the tower reported wind as inserted in the PERF APPR page.
The minimum energy level is represented by the Ground Speed the aircraft will have at touchdown. This Ground Speed is called "GROUND SPD MINI".
During the approach, the FMGS continuously computes the speed target using the wind experienced by the aircraft in order to keep the ground speed at or above the "Ground Speed Mini".
The lowest speed target is limited to VAPP.
The speed target is displayed on the PFD speed scale in magenta, when approach phase and managed speed are active. It is independent of the AP/FD and/or ATHR engagements.
Wind is a key factor in the ground speed mini function.
As you can see a tailwind will not have any affect on the Vapp target. Normally it's affect is transparent to the crew but during strong wind conditions the speed changes can be quite dramatic!