I am no expert but by 11 weeks they should be pretty much full grown. I put young birds in with the flock at around six weeks. They run around and get picked on a bit but as long as there is three or more they tend to stick together and adjust very quickly. My coop offers lots of hiding places for the young birds until they adjust but I have found they are mixing it up with the flock very quickly. Again it may depend on the type of bird. My birds are pretty laid back though there is a definate pecking order. That is the way with chickens, once established they harmonize very well. Again I am no expert and still pretty new to this but my mixed flock accepts young birds quite well, and if I have any troublesome bullies well as hard as it is they get culled.
Maybe I misunderstood and you were introducing 11 chicks that are 4 week old, in which case I would indeed be cautious, but 4 chicks 11 weeks old should be fine.
I too put my chicks in and area where they can see the older hens for a few weeks before I put them in, and I also put them in in the evening, and they don't have to leave their area until they want to but I really wouldn't worry if they are 11 weeks old.
I just release seven chicks that are about nine weeks old, two days ago. They were pretty scared and sleep in the nesting boxes but they are already hanging out with the other chicks two weeks older them them and are going outside and really enjoying life.
An amusing aside is that I have three great big blue orpington hens, they are sweet girls and I found they actually intervene on behalf of the young ones and put themselves between the young birds and the head hen and mediate.
Chickens are just so cool.
Again the size of coop and the type and number of birds will make a huge difference, you must be the judge. Good luck.