I have noticed that the most damage is when the garden is young. I successfully raise corn, yellow squash, cucumbers, eggplants, melons, irish potatoes, and more with freeranging chickens and ducks. The biggest issue I had this year was with rabbits eating the corn while it was small. I recommend either keeping them out of the garden while the plants are young (corn needs to be about 12 inches tall) or just fencing them out completely. So far my strategy has been to plant twice as much as I need and it has worked great for me.
On my tomatoes and squash last year the chickens did a great job of keeping the bugs off of them. First year I didn't have to spray at all. of course, there was peck marks on some of them, but I didn't care about the looks, I was eating them, not selling them. i tried unsuccessfully to grow peas and beans. chickens will eat them.