Thanks for citing my post!
Here's my two cents: I would say do introductions on a leash so that you have control. Also, I'd do the introductions in the cats' environment, so the dog walks in knowing it's their home. I've done that with my fosters and my dogs.
Riley came in as a puppy. Also, Thomas, the cat in the picture, is the dominant animal in the house. I also have two of his brothers-Turbo and Bevo (rescued all of them together)-and Turbo is second in line, then Riley, then Sadie. Bevo doesn't seem to be aware that there is a power structure. LOL Thomas can just look at the dogs a certain way, and they walk away. Turbo, however, will hiss and whatnot, which excites the dogs. Then he ends up running off, b/c they're trying to play. I still think he's dominant, though, b/c he can walk down the hallway and they will move for him. Bevo will get chased sometimes, but he generally stays out of the dogs' way.
So I guess it depends on a few things: the tempraments of the dog and the cats (sounds like the cats are okay with your other dog) and the heirarchy. If the dog wants to play with the cats like my dogs, it helps if the cat is dominant and can stop the situation when it wants. If the dog is indifferent, then the only way it will impact the cats is if they are afraid of her size; however, you already have a fairly large dog, so that seems like it won't be an issue. If the dog has issues with cats like aggression, then that particular dog may not be right for your home. But that doesn't mean there won't be a Saint out there who is right for your home.
One more of Thomas and Riley: