I found the same as L4H, it depends on the personalities involved. I've had it work and not work.
A male rescue we took in got his nose in a snit when a cute little girly kitten showed up. He'd play happily with us, US, the human people, but when he realized Miss cute kitten was in the room he'd turn and stalk out. It was kind of funny to see. He never hurt her. After about a year they became best friends.
Our current 18 year old Ginger has never adapted to the newer cats, Sadie and Bitty. We've had them all for 12 years. Ginger hates them and Bitty in particular hates her to the point we've had big Vet bills and have to keep them separated. Ginger is fine with the dog, but took a year to feel comfortable with his royal highness harum, scarum puppy.
You can't tell ahead of time how it's going to play.