Yes, the chickens will fertilize everything and everywhere!
I have four, seven months old hens and I cannot believe the mess they make.
Our suburban lot is almost a quarter of an acre. We have a large front yard set back; the hens live in a playhouse and 5'x13' attached run. I wish I had a larger run for them, and then I would rarely let them out of the run in our back yard. Their favorite activity is sitting on the bricks at the back sliding glass window, waiting for treats. They sit and preen their feathers, occasionally tapping the glass (as if I weren't aware of them there!), and fertilize everything.
You didn't state your children's ages. I have nine kids (youngest 17 years) and they think the chickens are pretty hilarious at times, especially with our cat outside attempting to pounce and getting a good peck/feathers in the face for all his trouble. They are fun to hold, but it's hard for young children to do this. And feeding them treats make my grandchildren nervous.... they will scatter raisins at the hens, but don't hold out their hands to feed the hens. Those beaks can hurt!
Everyone thinks it's fun to collect eggs, though!
I would purchase docile breeds of chickens, and unless you have a few acres at least, build a very large run for the chickens. Your children will be able to go inside it to see the chickens when they want (keep special shoes outside the run for the kids to slip on while inside), and they may run around outside the run without worrying what they'll be tracking into the house.
Carla