Unfortunately, no. When the great Schism happened, there were two primary Covenant factions, the loyalists who stayed with Truth and Mercy, and a large Sangheili-based faction led by Supreme Commander Xytan 'Jar Wattinree. Xytan's faction was ultimately destroyed when a Huragok repaired a NOVA bomb taken from Reach, obliterating the colony Joyous Exultation and its moon, along with a large portion of the nearby fleet. When the Covenant led by Truth was finally defeated, the next Covenant to rise was the one created by Jul 'Mdama. Around a similar time, the warlord Merg 'Vol also assembled his own Covenant and attacked the UNSC colony of Dratheus V. Meanwhile, a Brute-led Covenant faction called Keeper of the One Freedom was created. Beyond those three, it was mentioned that dozens of Sangheili warlords have carved out groups that they claim to be the Covenant.

[quote]Huragok[/quote] wat

I can only hope a bunch of them are more focused on arguing which is the true new Covenant.