Without a doubt, chickens are very hard on grass, even around the coop, if you let them out.
Everyone on here has a different set up, so I am just guessing...if you live in town, and want to have a grassy area, then it would probably be best to confine your chickens to a single spot, which will become grass less, and only let them out over the grassy parts for a small part of the day.
Chickens do poo a lot, so if you have children playing in the grassy area, you may not want to have the chickens in that area too, and chickens will love to sit on decks and patios, pooping there too.
3 chickens will cause less damage than more chickens, but over time, they will destroy most vegetation, unless you have a VERY large area to rotate the tractor coop, and it will have to be done with a great deal of regularity, so if you are gone for a day or two, could cause some damage.