If the Fertilizer is on the Ancient Fruit's soil at the time you harvest it, the fruit quality will benefit from the Fertilizer. Since crops never die in the Greenhouse, that Fertilizer will work permanently on your Ancient Fruit plants. However if you process Ancient Fruit into Wine or Jelly, you lose the benefit of any quality improvements from that fertilizer
so you could consider using some kind of Speed-Gro if you plan to process everything. Since I process all my Ancient Fruit, I use Deluxe Speed-Gro so I get more harvests and therefore more g from the increased amount of Ancient Fruit Wine and Jelly I make.
What
@One More Day said below. I mixed it up with replanting the 12-13 day crops where they shorten to 10 day grow time with Deluxe Speed-Gro to get 3 harvests in per season.