I haven't observed that denouncing, waiting and then DOWing makes much, if any, difference with the other civs, but others may have observed a meaningful benefit. Goading the AI into DOWing you is very beneficial, however.
Denouncing will change the denouncee's (I think that is a word) attitude towards you. It always enrages them, but may or may not be enough to get them to DOW you. Combine it with a series of unreasonable demands (stop settling near me, give me city X, give me city X and Y, give me all your gold, etc.), converting their cities (if they have their own religion), stealing their CS allies, and other provocative diplomatic actions might be enough to get them to DOW you.
Of course, it might also result in them bribing 3 other civs to DOW you too, so be prepared.