I never ever pick the fruit from the trees - once in a blue moon, I'll sell an apple.... I never pull the veggies either. I just leave them.
That's fine on the veggies. The peeps will eat them on their own, about one veggie/peep/day. When you have a lot of peeps, make sure they don't eat all the veggies when you're not looking! Of course, there's a quick 90 minute fix for that - plant more veggies.
As for fruits, look at the life cycle of an apple. It starts as a flower on the apple tree, matures to an attached fruit, falls to the ground, and finally disappears. Each of these stages takes about a day. Note in particular that fruit on the ground disappears the next day.
Fruit on the ground counts toward total available food, visible in the Food Status (tap on the Cornucopia). The apple will become unavailable as food in one of three ways: if a peep eats it, if the mayor collects it (i.e. you pick it up), or if a new day starts. When the fruit is in the mayor's inventory or storage, it disappears from the total in Food Status. But when you SELL the fruit to the store, it reappears in Food Status and counts toward available food. AND, you have 25 coins more to spend.
With three fruits every three days, a tree pays for itself in about a week, and after that it's just gravy. My orchard is a cash cow for me, it's just distressingly far away from town, especially as I need to make 2 or 3 trips to harvest it all.
Most fruit is worth 25 coins per piece. Some fruits are worth much more.