I believe the big name hatcheries don't allow visitors to wander about without taking some biosecurity precautions, so even if you're going to pick up chicks directly from them, they might just hand you your order instead of having you walk around the facility. (I don't know for sure, no hatcheries anywhere near me to verify this against).
Feed stores on the other hand, yes technically people can walk in wearing whatever they just came from their farm in, though a good store will manage the chick area so only employees handle the chicks, to minimize contact.