The Plurality of Worlds Messal turns out to be plenty influential in the Convox.
It's got six Edharians, who are the stars of the Convox, and one of whom is a Millenarian, its got the top Procian of the mathic world, it has
the most accomplished Incanter and Rhetor
of the Convox, and thus probably the entire mathic world, and of course, it has Fraa Zh'vaern, who is
unmasked as the alien Jules Verne Durand of Earth from an alternate universe.
(OK, that's enough spoiler-text for the question page snippet ... if you read on you agree you've already read Anathem).
That collection of top-notch avouts in a late-created Messal leads to a number of questions, but let's start with:
Why did Fraa Lodoghir tell Fraa Erasmas, before any meeting of the Messal (but after he was informed of it, and presumably, also of the attendees), that he considered it the "outer darkness - the arse-end of the mathic world"? Did he believe that, or was it a cover for his knowledge that incanting and rhetoring would be key to resolving the crisis facing Arbre, or something else?