Yes, denouncing them can help a lot!
The AI seems to want the element of surprise and this action seems to make them think twice. It probably has some relation with their personality as well, so It might not work on Shaka, because nothing does.
Before you do this, take a look at the global politics information.
1) Do you have a DoF with them? backstabbing is bad, so maybe dont do it.
2) Have one or two leaders already denounced them? Adding your voices together can often prevent the attack, or at least delay it. once the other leaders see your agreeable stance, maybe they will become more easily bribed into DoW-ing the aggressor, and then you can sit back and build units for a while, which should put the whole situation to rest.
Interesting, I might just have to try this. Although you say it take multiple denounces from more than 1 Civ. I'm not sure if that would help you if you spawned in jungle and you had Rome 16 tiles away with iron who immediately covets your land?