Chickens do fine with pigeons, but sometimes the pigeons ca nget a bit aggresive to the chickens. So I would say its ok to keep them together ....But do not put a broody hen with pigeons, she will go crazzy all the time thinking the pigeons are hawks or something.
I have pigeons with my chickens. The chickens ignore them for the most part. Every once in a while I will catch a hen chasing the pigeons. Seems to be a game for them.
After a short time the chickens recognize the pigeons as harmless, even when flying. My broodies pay them no attention at all.