That depends entirely on the cats. You won't socialize Puddles with any cat, she won't even tolerate Jasper, who has been allowed immediate access to every foster litter I've had by the kitty momma. That's how friendly he is.
Sweet Pea, who is only semi social with other cats, can be socialized with other cats who allow HER to be the boss.
And Jasper, well, can throw him in with pretty much any cat (except Puddles) and they just LOVE him to death.
I so agree with holding off on getting the dog, it will be enough on the cats just to get used to each other for now. And slow intros are always the way to go, gives both cats a chance to get used to each other's smells.
Have you suggested feeding the cats on each side of a closed door, so they get positive feelings while being close but not being able seeing each other?
Do they have their own cat stands that they can claim for their own territory?