Yes. Except that it wasn't *one* mutant gene but a long string of them betweenthe common gorilla/human ancestor and modern gorillas/humans.
OK, look at it this way:
Not the best example of a cat morphing into a dog I've ever seen, but it's the best I could find at short notice. The point: at the beginning, it's clearly a cat. At the end, it's clearly a dog. But when does the cat become a dog? There is no single definable step between them. The illustration would be better if the animation was better, but you get the idea. Over many hundreds or thousands of generations, small changes accumulate.
> And the line bred true and separated later somehow so that human anthropoids could no longer breed with humanoids. Fantasic. What are the odds on that happening--and the very small genealogical line being unbroken in the early years by disease or violent death? Could have ended at any time.
Yes, and many such offshoots do in fact die out. Horses, for example, evolved in the Americas and then crossed the Beringia landbridge during one of the ice ages... and then died out in the Americas, only re-introduced with the Spaniards.
> How often do gene mutations that survive occur?
Rather often.
> Is there any documentation on that?
I've seen that, yes. Hop over to Google and do a search.