What are the chances?

I have a feral mother cat and her latest litter of four in a large dog cage in my bedroom. They were neutered on Monday and I am keeping them for a while until I see that they are healing OK. They are all afraid of me but they don't panic when I approach them or clean their litter box. I am surprised at how well they use the litter box and carefully cover everything. I stood the dog crate on end and had it fixed with three additional levels of floors. The top level is easiest for me to reach so that is where I put the food. The next level down is a slab of Styrofoam and momma claims it most of the time. There is one little girl and she often sleeps with momma. The first level up and the bottom level with the potty box are shared by the three boys. They all are still doing a loot of sleeping but often one will wake up and start to play with the strings that are holding everything together, then before long they are all awake and playing. Before long they drop off to sleep again.

So if I replace the door of this room with a screen door (it is my bedroom) is there hope that they will accept me eventually?