Or Nanclus could simply be bringing promises of Romulan aid (cloaking devices for rescuing Kirk from the heart of the Klingon Empire?) to one side of the upcoming war, or at least promises of neutrality in such a conflict - thereby facilitating the conflict in the first place.
True, but then he wouldn't be standing there in the President's office giving legal advice while the Klingon ambassador barking about the extradition of Kirk. That would earn him at least one pointed "What the fuck are YOU doing here?" remark.
What's significant is that nobody thinks it's odd for Nonclus to be in that office or to be present for that confidential briefing. Relations between the Federation and Romulus were never THAT good.
Remember that in this three-party conspiracy, everybody must have believed that their side would win and the other two would lose - but the cabal could only be held together by everybody claiming that at least one of the others would triumph in addition. A third party would be an utterly vital element here, as it would be rather impossible for Cartwright to convince Chang that the Feds would help start the war so that both sides could win! (Sure, there's that universal fear of soldiers that peace will make them unemployed, but that wouldn't be enough to drive the conspiracy; a hope of victory must have been an ingredient there.)
Makes sense either way. Nonclus would have wanted the Klingons to get the hell off of his planet one way or the other and having the Federation crush them in a one-sided war is a good way to accomplish that. More importantly, it would have exhausted the Federation to the point that Romulus' long-awaited coming out party would be that much sweeter.
As it stands, they were able to break out anyway after the Klingon Empire fell, but by all accounts they were never able to really threaten the Federation until the Tomed Incident many years later. It wasn't the decisive victory they'd hoped for, but it DID result in the Federation abstaining from using cloaking technology.