I square foot veggie garden and the veggie garden is fenced by four foot fencing which is loose at the top so nothing likes to land on it because it is wobbly. Last night I came home to a veggie garden massacre. Don't know how the BO's got in,they can't even fly to the top of their roost and need steps but they were freaking out when I got home because it was time to roost and they couldn't get out. I opened the gate and they ran to bed. I then surveyed my damages. Lost an entire box of beets and celery, 1/2 a box of spinach and carrots, 1/2 of my kale, the cauliflower looks like skeletons, all my 'nearly' ripe tomatoes are gone and so on. From my perspective, with my big girls, I'd make every effort to seal them away from that which you are growing for yourself.
However, the little OEG's I have aren't a problem in the garden, in general. They don't move as much dirt as the six BO's and don't eat as much. If I have a box that is newly seeded and I don't want the OEG's to spoil it, I cover it with chicken wire until the plants are up enough to make it. My BO's can rototill a 10 inch deep box in a very short amount of time. Even with the OEG's patroling, I still get some bugs. Primarily beetles that are distasteful to the birds like stink bugs.