Of course nothing is "always." All we can offer is the majority of cases we know of. It would be wonderful to save an older cat. Maleke, when you go, one of the cats or kittens will speak to your heart. Try to find out the history of the adult cat. Find out if it was an only cat, if you can. Get as much information as possible.
In my personal experience my adult cats accepted kittens better than another adult cat, and the littermates I've raised together were a lot closer than my sister and I ever were!
When I had only a single adult, my son's cat, for a year, he never accepted the two kittens (they're grown up now.) I now have. He hissed at them, and chased them, but never hurt them. When the kittens grew up they ganged up on him. He started to run out the door and not come back for a week at a time. Although he had bullied the kittens, I felt sorry for him, and when he came home, I would protect him and give him canned food and lots of attention. Nevertheless, he finally left for good.
That's the only time I've had that much trouble. He had been an only cat too long, I guess. Just before that I had four cats, and each was an adult when the next kitten was rescued.