I think it's a bit hard to say... even if the cat and the dog
were together since they were young.
Anyway, let me share my experience.
I used to have both cats and dog under the same roof.
Cat A came when it was a weak kitten and we put it in the Dog's
cage. The kitten was weak and unable to retaliate or express
displeasure whenever the dog went near the cage to sniff
sniff.
As Cat A grew older, it became good friends with the Dog. Each time
they met, they would mingle with each other (even though most of
the time it's more of the Dog ka-cheowing the cat by sniffing here
and there while the Cat bochup).
Now Cat B came to the house a few months after (still a kitten, but
a bigger kitten). Right from the start, my dog was hostile towards
Cat B and they NEVER got along well and even had a brawl once
(thankfully none were injured). My dog would ALWAYS chase Cat B
whenever she got a chance to.