Shadrach would say like is attracted to like. Me, I think you need to define your terms/expectations a little better. If you mean by *one big happy flock* will they all potter along together with minimal jostling & pecking, I would say YES! If you mean will they all like each other & socialise with each other ~ probably not.

Just like people chickens have personal likes & dislikes & some chickens will never get along with each other. Others tend to be more distant. Some get on with anybody. Some of how your flock settles will depend on breed characteristics & then individual personalities.
As you know, I've just done an integration. My flock has settled really well & I am happy with how it is functioning. It is calm & peaceful but the pecking order is rigid. My Rocks are on top @ present & then the Australorps. The Rocks hang with the Rocks but are OK with the Australorps ~ they were my original flock. Those 4 are ok with the Favorelles [who are pretty calm & docile] but can get savage with the Campines if they consider they've stepped out of line. Everyone harries Lottie because she is tiny & the Campines get harried as well but aren't on the bottom ~ just the other chickens find them pushy.

Lavender & Patricia are sort of outsiders but accepted overall. They are usually last to eat or get tid~bits. No~one is outright ostracized, but within the flock friendships are forming ~ usually like with like. Give it time.

All will be well.