Chad! I think you're on to something
I am holding down shift (sprint) and yes, I tested it now, when I do a drive by and pick up fruits my "food" goes up!
So in order to farm I need to stop sprinting?
Try it, and look up into inventory. 🙂
Yes, you're even given a tutorial that you will equip the item by pressing Trigger + Sprint Buttons.
Look at your stats if you ate something. (SAT for Food and STA with the White Dragon Flower.)