You can try it. They might scratch all the hay out, or they might be fine with them. They also ight lay in the corner of the stall, or wherever they want, though!
Is there a roost in there that is higher than the nests? It would be a good idea, as they will usually sleep on the highest point, and you don't want them sleeping in the nest boxes or you will wind up with poopy eggs. Be sure the roost has some width, like the wide side of a 2x4 or a fat branch, for the comfort of their feet.
We have fenced the back area so they can get out and run around in the grass, it is about 6 ft wide and 10 feet wide. They will go out the door that is blocked, we have run wire to cover the door for predators and cut a small opening for them to come in and out.
Wow.. it's palatial. My chickens would be so jealous. We built ours into an existing barn, too. I think they would prefer boxes that are closed in on the sides and top for privacy. They hide their nests in the wild. Milk crates on their sides and covered with cloth would be inexpensive. Although they will probably sit on top of them and make a mess. I do worry about the wire I see on the door. Predators that are hungry can easily tear through wire with openings that size. We covered all openings of the coop (except the chicken door to the run) with a double layer of hardware cloth. The mesh is about 3/8 inch and it is very sturdy. We also put two locks on the inside of the chicken door which we latch at night to keep predators out. Knock on wood, but we've not lost one yet.
P.S. I hope you realize the table will be destroyed in a few months? Cover it with a vinyl tablecloth?
Thank you!! We will get some chicken wire and put it up over the other wire. Thank you for pointing that out. I am so glad I have reliable sources to help out with this. And the table is what it is for. But the milk crate idea is better than the little ones that we have there. I have some that I can use.