E.g., no - upon arrival of front gust it does not add thrust.
From Airbus A320/321 FCOM:
GROUND SPEED MINI FUNCTION PRINCIPLEThe objective of the Ground Speed Mini function is to take advantage of the aircraft inertia, when the wind varies during the approach. This objective is achieved by providing the adequate indicated speed target (i.e. the managed speed target represented by the magenta triangle). When the aircraft flies this indicated air speed target, the energy of the aircraft is maintained above a minimum level ensuring aerodynamic margins versus stall.
During the approach, the FG continuously computes the managed speed target in order to take into account the gusts or wind changes.
my bold
I might be missing something, but am struggling to understand how the aircraft would follow an increased managed speed target from GS Mini, without increasing the thrust?
Or maybe my semantics are in question? With a gust, the FG computes a new managed speed target, which the auto-thrust follows, (if it is engaged). i.e. GS Mini itself does not add thrust, but it dynamically changes the managed speed bug, which then causes the auto-thrust to add thrust if required.