To understand the Organians and the treaty situation, you may want to consider these passages from "Errand of Mercy":
(with thanks again to Chakoteya.net transcriptions)
...and also this passage from Act 1:
...and then there's this from Act 4:
Given that Trefayne seems to know what the Klingons are up to, but only announces what he knows once the enemy fleet assumes orbit, we can assume the Organians are (mostly) concerned with how the conflict affects them on their planet. Ayelborne and Claymare seem to infer they have the power to paralyze the entire Federation and Klingon Empire, all at once, and are already doing so, but that they don't want to interfere. Most telling is that Ayelborne and Claymare seem to be complaining that the Organians find the "mere presence" of Kirk, Kor and company to be "intensely painful" asking them to leave. Spock's comment in the Teaser makes it clear that the hostilities have focused on "the only Class M planet in the Disputed Area, strategically located for either side", and the Organians' hot tomale/paralysis trick makes it clear neither side is going to have access to the planet, take the planet off the table and that diffuses the conflict immediately.
With the exception of subsequent mentions of the Organian Peace Treaty, we never hear mention of or see the Organians ever again. This tells me that the peace treaty is simply called Organian by the Federation and the Klingons because Ayelborne dictated terms before vanishing, Kirk and Kor reported what Ayelborne said to their respective superiors, and the language made it into a treaty negotiated by the warring parties without Organian participation. And I think the episode is clear that we are never expected to see the Organians ever again (at least not Ayelborne and company) as the characters deliberately transform into non-corporeal beings before everyone's eyes and are not heard from for the rest of the story. There is no disembodied "use the force, Luke" to imply these aliens are somehow still active participants after they disappeared.
So from all of this we can conclude that it is indeed possible that Federation and Klingon starships can do battle, or at least take an occasional potshot at each other. But both sides are probably worried that engaging in an all-out war, particularly with Organia apparently interposed between the Federation and the Empire, would risk of another confrontation with the Organians. This is obviously something both sides are deathly afraid of. With Romulans, Cardassians and other powers lurking about, neither side would want to find their fleets disabled for any period of time.
I also get the impression from Spock's and Ayelborne's comment in Act 4 that the Organians look upon humans, Klingons and the rest as if we were like bacteria or a fungus. They're capable of interacting with us, but they would prefer to avoid getting athlete's foot or diarrhea or whatever. So shoo... go 'way...
And both warring parties obviously knew this right from before the treaty was even written, as Kirk and the Klingons never hesitated to take up arms after that. Clearly, nobody was ever worried about Organians looking over their shoulders.
(with thanks again to Chakoteya.net transcriptions)
...and also this passage from Act 1:
...and then there's this from Act 4:
Given that Trefayne seems to know what the Klingons are up to, but only announces what he knows once the enemy fleet assumes orbit, we can assume the Organians are (mostly) concerned with how the conflict affects them on their planet. Ayelborne and Claymare seem to infer they have the power to paralyze the entire Federation and Klingon Empire, all at once, and are already doing so, but that they don't want to interfere. Most telling is that Ayelborne and Claymare seem to be complaining that the Organians find the "mere presence" of Kirk, Kor and company to be "intensely painful" asking them to leave. Spock's comment in the Teaser makes it clear that the hostilities have focused on "the only Class M planet in the Disputed Area, strategically located for either side", and the Organians' hot tomale/paralysis trick makes it clear neither side is going to have access to the planet, take the planet off the table and that diffuses the conflict immediately.
With the exception of subsequent mentions of the Organian Peace Treaty, we never hear mention of or see the Organians ever again. This tells me that the peace treaty is simply called Organian by the Federation and the Klingons because Ayelborne dictated terms before vanishing, Kirk and Kor reported what Ayelborne said to their respective superiors, and the language made it into a treaty negotiated by the warring parties without Organian participation. And I think the episode is clear that we are never expected to see the Organians ever again (at least not Ayelborne and company) as the characters deliberately transform into non-corporeal beings before everyone's eyes and are not heard from for the rest of the story. There is no disembodied "use the force, Luke" to imply these aliens are somehow still active participants after they disappeared.
So from all of this we can conclude that it is indeed possible that Federation and Klingon starships can do battle, or at least take an occasional potshot at each other. But both sides are probably worried that engaging in an all-out war, particularly with Organia apparently interposed between the Federation and the Empire, would risk of another confrontation with the Organians. This is obviously something both sides are deathly afraid of. With Romulans, Cardassians and other powers lurking about, neither side would want to find their fleets disabled for any period of time.
I also get the impression from Spock's and Ayelborne's comment in Act 4 that the Organians look upon humans, Klingons and the rest as if we were like bacteria or a fungus. They're capable of interacting with us, but they would prefer to avoid getting athlete's foot or diarrhea or whatever. So shoo... go 'way...
And both warring parties obviously knew this right from before the treaty was even written, as Kirk and the Klingons never hesitated to take up arms after that. Clearly, nobody was ever worried about Organians looking over their shoulders.
