Warning the Cardassians through a 3rd party, in this case Garak, was the right thing to do. Rescuing the Detapa Council, by engaging in battle with Klingon ships was also right. The UFP's directive, and Starfleets orders were broken for the greater good. Trying to keep the Klingons, and Cardassians from fighting a bloody war was the best thing for the AQ at that time.
Had the Klingons catured the entire Cardassian Empire, keeping it under their control would have cost them a large portion of their fleet and huge amounts of man (Klingon) power and resources.
The Dominion could have then come through the wormhole in force, overwhelming DS9. With the wormhole secured (I don't think the Federation had upgraded their shield technology to block Dominion weapons at this point.) they could have brought through a huge fleet of ships. The Klingons would have been too spread out to react and gather enough ships to defend the Empire. The Klingons would be out of the War.
The Cardassian Empire, already in disarray after being conquered by the Klingons, would not be able to resist the Dominion forces. 2 AQ powers down.
The wormhole, now more tightly secured, would leave the the Dominion free to keep on bringing in ships. Sacrifice of Angels
told us that a fleet large enough to defeat the combined Klingon/Federation fleets was coming through, that would suggest that the Dominion had more ships than the Klingons and Federation combined. The Federation would have been conquered. 3 AQ powers down. The Federation and Klingons make up 2 of the "Big Three" AQ powers.
Would the Romulans join the War on the Federation side? Doubtful, they would most likely try to seek a way to stay neutral, even if it meant becoming a satellite republic of the Dominion. Yes that is speculation, but with the 2 of the 3 strongest powers defeated, the Romulans would have little choice.
That's how I see it anyway.