I've gotten food bonuses with just tomatoes in the fridge. A mac and cheese with a tomato became a satisfying meal even for the near starved. Once the vegetable or fruit goes into the fridge it looses the original identity and becomes "fresh food".
So, what type of produce you put in the fridge doesn't matter in the making of dishes. However, an eggplant may add more fresh food points than tomato (haven't gotten that far with gardening yet

).
You can have a fridge full of fresh food, but, I'd think, without the normal stock you won't be able to prepare a meal (again, haven't gotten that far, but since there's no new dishes based on the various produce and it's a separate category when checking the food levels, it sounds logical.
Echo made some vegetable and fruit plants/trees that could be harvested and use to restock the fridge. Unless she's updating them to make them act as the Seasons plants and tress, they should continue to increase food stockage and not add to the fresh produce levels