Ahh but that's the problem. Destroying the Emperor and the Golden Throne is the main quest. It is a war of symbolism...and true symbolism must be accomplished directly. Bombard the Palace of Terra to ruin and you have no sure way of confirming its destruction. A ground assault is the only real answer especially when it comes to Chaos. Have you once seen a Chaos crusade not fight things on the ground because they value sacrifices that they can collect from. The carnage, the suffering, the emotions from which they can grasp with their hands as they send their enemies screaming to the warp? No Chaos commander would forgo that and that is why Abbadon would never win this fight. I will cede the point that the Imperium of Man will eventually fall. But it won't be to Chaos....no the Imperium of Man will fall to itself of its own free will and while Chaos will continue to exist, it will never be able to fulfill the dream of making Terra burn. Edit: Since Du'un ninja'd my post: Yes the Imperium of Man will fall in the future but it will be long past anyones lifetime. Plus the original postage is Abbadon himself accomplishing this which is physically impossible even for one such as him. If he were to say create a Chaos commander duplicate of Creed, then Chaos would probably win because Creed is OP and he needs a ban hammer.
Eh, I think the Warp flooding into reality and daemons starting to pour out and slaughter all the citizenry of Holy Terra would be a pretty clear sign of success. They don't even really need to slay the Emperor for it to work, all they have to do is damage the machinery of the Golden Throne and cause the Astronomicon to falter and it's pretty much game over for the entire system. And from what ABD has established in Talon of Horus, Abbadon is perfectly willing to win a quick and dirty victory. When he founded the Black Legion his first victory was literally to just crash a starship into the Emperor's Children's base in a surprise attack.
Couple of things: Which Daemon Primarchs are returning to lead their once legions? Angron was like the last iirc back in Armageddon's first war, which was an age ago. As far as I know, the Daemon Primarch's are far more involved with taking part in the Great Game than leading further incursions into Imperial controlled space. Incidentally, I wouldn't list Armageddon as an export world given that it's currently getting pounded hard by Orks, and I think that planet could go either way. I also strongly doubt personally that the Tau recognize 'Chaos as a true threat' on account that they understand even less of Chaos than the humans do. The Tau do not have a warp presence after all, and tbh I think their thought process leans more towards: "what's the big deal anyway?"
If Cadia falls, Abaddon will have no problem destroying the entire imperium. Let's remember the section of the Black Legion codex entitled "The Crimson Path". It is stated that once the Necron structures known only as Pylons are destroyed on Cadia, the Eye of Terror will no longer be held at bay by the Necron technology, and basically the entire Segmentum Obscurus becomes the Eye of Terror. Then, Daemonic Legions will be able to swarm into reality with little to no hindrance, and perhaps they may even annihilate the Tyranids. (hopefully for Chaos) If Cadia falls, everyone who isn't Chaos, even the Tyranids, are screwed by Daemons.