I notice this is your first post. Welcome to the forum.
I forsee some potential problems, dust, smell, and possibly vermin. Not that it can't be done, but you'd have to actively manage these.
Chickens are dusty. They give off a lot of dander from their feathers. They scratch, take dust baths, and just create a lot of dust. No matter what you do, I think you will find a lot of dust in the coop. If it gets at all damp or builds up, chicken poo will smell.
For this to work, you have to have a dust-proof barrier between your living area and them. Otherwise it is not healthy. I would not have an inside door to the coop. I would have access to the coop only from outside.
You will have to have an active poo management plan. Chickens will drop between a third and half their daily poo while roosting. I have seen it managed where the smell is almost not noticeable but it has to be kept dry and not allowed to build up. With 4 bantams, I think you should consider removing the droppings daily. This could mean installing a droppings board and scrape the poo daily. For a droppings board, think a solid floor like plywood covered with linoleum so it is easy to scrape off. You might come up with something different, but think of how to remove the poo daily. You also need a place to put the poo when you remove it. I think most of us use some version of a compost heap but your circumstances may not allow this.
Chicken poo will attract flies. Another reason to remove the poo daily. The chickens will eat some but they will not get them all. Where you feed will attract mice and rats. Do not feed in the coop.
You mentioned that you will have only 4 bantams and all they will use the coop for is sleeping. This means your nesting box (one will be enough) and food and water will be outside. You do not need 4 square feet per bird in this coop. I don't know the absolute minimum you could get away with, but I'd be thinking more on the order of 1 square foot per bird if you let them outside as soon as they wake up and you don't allow them access during the day. Think an area maybe 4 feet long, 1 foot deep, and 3 feet high with an opening that lifts up to expose the entire length for ease of cleaning. I'd put a roost maybe 6" off the floor so they would sleep up out of their poo. I'd have the height above them to allow for installing ventillation above them so they are not ina draft. It will need ventilation.
Is it doable? Yes, I think so. You will have to actively manage it and thoroughly think it out. I have never done it so these are my thoughts, not my experience. Hopefully others will come up with other ideas and experience to help you out.
Good luck!
