If this point has already been mentioned, hey I'm sorry. Please bear with it though.
In Yesterday's Enterprise, the destruction of the outpost on Narendra III is what led to the war between the Federation and the Klingon Empire. As far as I know, the exact chain of events that led to war was never revealed. However, I always assumed anyway that the Federation was blamed for complicity of some kind, while in the restored time line, the sacrifice of the Enterprise-C undermined belief in such complicity.
Therefore, it is entirely possible, is it it not, that in the alternate timeline of YE, the Klingons could have gained allies against the Federation, because they too perhaps even reasonably believed that the Federation was complicit? It is not established in YE whether allies have shifted from the Federation to the Empire, not only because they are afraid of the Klingons, but also because they no longer believe in the morality of the Federation.
This is why the circumstances of the cause of a war between the Federation and the Klingon Empire are important to the question. It's also why using YE as a benchmark isn't accurate, except maybe to resolve the question with respect to similar triggers which could have undermined belief in the Federation's good intentions.
There is no evidence at all to support either the Klingons or the Federation having allies in the war. From what we see in the episode, it was just Klingons vs. the Federation and the Federation was loosing. On the whole, I would say Yesterday's Enterprise is an accurate benchmark on what a sustained Federation-Klingon war would be like. It doesn't matter how the war started, it only matters that the war happened.