I would not do that. They do not need to be in that nesting box. She will take the chicks out and take them to the feeders and the water. Put them in the back side of the coop so that she has to walk across the coop to get to them.some chick water/food feeders from when we raised these hens so I can put those in the nesting box
Your biggest problem is going to be when she wants to take them out of that elevated coop. Chicks always have a difficult time navigating ramps and sometimes the mother just doesn't realize they're not following her up. Or some will go up and the other stay down and now she's got chicks all over the place and can't manage it. You're going to have to help her out with that part.
Your coop really isn't that big for the number of birds you're going to have. You better have a plan for the cockerels because their father won't tolerate them for that long of the flock.