If you have a really nice really big run that they also have access to 24/7, feed and water outside, and with your remote nest boxes it might possibly work. In other words if that is just used for weather protection when sleeping and any time they are awake they are not in there. Otherwise no, 15 is ridiculous. Fifteen chickens in that is industrial management techniques and chickens specially bred to withstand those conditions. We treat our chickens better than that. Very few of us even understand the complexity of what industry has to do to make that work. It’s not easy. I’m not even sure you could get enough roost space in there for fifteen chickens.
There are a whole lot of factors that influence how many chickens you could use that coop for. Size of chickens, individual personality of each bird, flock make-up including sex and ages, climate, how you manage them, and many others. If you want you can follow the link in my signature for some of my thoughts.