A heavy 321 is a bit of an energy pig. I only flew 321's for about 600 hours. Brand new ones. Where I flew them we had tailwinds on approach almost half the time. But, it was usually smooth.
I would guess that the ultimate test of the autothrust on 320 series aircraft would be a heavy 321 with a tailwind, in gusty conditions. I didn't do that very much. Almost none.
But even on a 319 or 20, they do OK in light to moderate gusty conditions. In Moderate to heavy turbulence, they just can't handle it. They do "do it" better than any Boeing, including the 777. But the organic operator is still expected to be better.
If your airline allows it, practice your skill set. If not, be ready to hit TOGA or the autothrust button, whichever comes first.
I do know that some carriers don't let pilots fly airbus with autothrust off. They are paying you so you have to follow their SOP.
AB autothrust is the best. It is just not perfect yet.