We let the cats up on furniture the dog is not allowed on. Works fine for us. As a matter of fact one cat regularly takes over the dog's bed and keeps him off it and no controversy ensues because of it. He's not a meek, mild dog either.
But, in a previous time with another dog and cat it would definitely have been a problem for us. And was as we had to keep dog and cat separated, which we managed for 10 years.
So my suggestion is keep an eye out. I think if there is no problem now there won't be but none of us can read a dog's mind.