So here is a interesting Alternate timeline.
So go back to the final mission of halo 2, the arbiter is talking to Tartarus. And he sees Thel’s point for whatever reason. The two agree, and a faction of the brutes break off and join Tartarus, whom himself joins the Covenant separatists, what would happen then?
Then we wouldn’t have had an annoying end boss fight or most of Halo 3’s events happening.
I’m pretty sure he knew the Arbiter was telling the truth, but chose to reject it because of the animosity between the two races, and because the San 'Shyuum were giving the Brutes the status and equipment previously reserved for the Sangheilli.
But if Tartarus left the Covenant, given how he’s the highest-ranked Jiralhanae, similarly to how the Arbiter is historically the highest ranked Sangheilli, there wouldn’t be much of a covenant left. With the Brutes and Elites split off, taking all of their Grunts with them, the remaining races wouldn’t really stand a chance. In all likelyhood the Separatists would form some sort of treaty with Humanity, and both sides would still have factions within them trying to undermine the other faction, due to fear of the other faction growing too powerful. Ironically, the attempts to limit the power of the other side are more likely to ignite armed conflict than just dealing fairly with each other.
JNDreher elaborated on this hypothetical well. Jiralhanae were the sole remaining backbone of the Covenant once Truth decided to rip his own foot off by backstabbing the Sangheili. Take them away and you’re left with whatever Grunts, Jackals, Drones, and Hunters who haven’t left for greener/more sensible pastures. Humanity by itself might be able to hold the line if only for a while against those odds.
It is possible that a segment of the Jiralhanae could remain loyal to Truth in spite of their Chieftain becoming a turncoat. Most of the species were rigidly devout to the Covenant dogma. You would have a difficult time persuading these devout creatures into abandoning the theocratic institution they were brought up in based on the word of a single Jiralhanae, albeit one with the most prestigious title of their race. Plus, to go from being elevated to the top of the Covenant food chain for the first time in Covenant history to now being made to stand shoulder-to-shoulder with your hated adversary and humans, I can’t see that going over too well with a number of Brutes.
My guess is that the Covenant would be splintered even further with some Jiralhanae aligning with Tartarus, a good number (the plurality maybe) remaining loyal to Truth, and perhaps some forming their own separate factions to fight against both the Covenant and the Sangheili/humans.
I think the war would dissolve into a multi-sided clutter of different groups trying to eliminate the others.
Humanity/Sangheili & Chieftain-aligned Jiralhanae (operating more like co-belligerents than direct allies since they still hate Sangheili) vs Covenant vs Jiralhanae Separatists
IF TarTar Sauce belives the arbiter, Then there is a good chance a lot of brutes would follow him. The covenant war would end. A massive power vacuum would also form. There would probably be a breif union to deal with the flood, wether it involves humans or is just between the separatist elites and brutes in up to debate however.
If Tartarus believed the Arbiter straight away, there would have been a narrative problem. There’s a subtle parallel between Tartarus and the Arbiter that is occasionally overlooked. The Arbiter faced an enemy early on in the game, Sesa Refumee, who was an outspoken critic of the Prophets. The Arbiter’s faith wasn’t shaken at that point. He was still a loyal servant of the Covenant. Nonetheless, Sesa provided the first opportunity for the Arbiter to honestly question his loyalty.
At the end of the game, the roles switched somewhat and the Arbiter took the place of Sesa when he spoke with Tartarus, trying his best to convince Tartarus that he was on the wrong side. But just as the Arbiter wasn’t ready to change his mind when he faced Sesa, Tartarus wasn’t ready to change his mind when he faced the Arbiter.
If Tartarus switched sides so easily, it would have become confusing from a narrative perspective as to why it took a whole damn game to get the Arbiter to do the same.