...and if you are going to do rotational grazing, look into rotational planting as well. Legume - Root - Fruit - Leaf - Repeat. Which really means 6 sections, not four, so you have one for the chickens, and one being prepared for the new planting.
If you divide the garden into fenced areas, rotate the chickens thru, following behind with your weeding/mulching/planting/harvesting in a rotational gardening process, you can make that work, yes. Most don't want to dig in soils recently filled with chicken droppings - your post gardening...
The best way to combine chickens and a garden is in the soup pot. Nor are they "free range" as you describe. To concentrate the nutrients you want from the chicken droppings, they need to be penned in your garden area (which they will destroy to bare dirt/earth). But as @ChickenCanoe says...