If you look up anti microbial properties of garlic you can find a lot of studies done on it, though not on chickens that I am aware of.
It makes sense that as an addition to a healthy diet it would be good. I would not rely on garlic alone to treat a case of parasites however. I'd also be careful about how much garlic (or any plant in the onion family) is given, again i haven't seen studies done on chickens, or birds in general, but large amounts can cause a loss of red cells in some animals, such as dogs. If cooked it causes less issues, however, I'd hazard a guess the properties loss during cooking maybe the same ones which kill parasites.
I don't add it to my chickens diet as a regular thing, however if I make something that has garlic in it for the family and I'm giving out left overs I will share with them and not worry. The only thing I worry about from my regular cooking and don't share is things with avocado's or chocolate in it.