Close, but not quite. Pacifica and IRON, out of frustration, had already written off Polar when they intervened, and RFI had infrastructure in place for responding to a Polar counter before the war even started (because unlike Oculus we observed two years prior that Polaris was not as on board with Oculus as the rest of their bloc pretended they were).
The issue was that the Legion didn't want to see Polar on the other side, so at their urging to RFI the summit meeting was agreed to. There was, at no point, a consideration of 'preserving the hegemony' involved, it was RFI's consideration for the Legion. That is why Pacifica and IRON said basically nothing throughout the procedure. Had the peace summit produced a result that was deemed unacceptable, the war would have continued, however Buuyo managed to work with deathbiter and myself to come up with what was ultimately signed. That's why there was outrage over the "super clever maneuver" of trying to avoid adhering to the intent of including GATO and Argent in the Boognish counter declares (the actual DoWs, not individual nations wars). It had nothing to do with "oh no they're dogpiling CLAWS!" and everything to do with the Legion knowing full well that it was going to undo the peace deathbiter had burned a ton of his own political capital to secure.
Lyanna's late night decision to "fix" that issue was the thing that ultimately secured that peace you very nearly torpedoed without even realizing it.