OK. Maybe this works even though they've walked out. (And it doesn't seem as if the broadcast had already started.)
Somebody in the comments provided a handy link that turned out to be only a few pages off from a partial explanation of what Numair's up to, which I'd forgotten the details of. Start here (or a few pages back from there) and read forward an additional few pages:
http://www.white-noise-comic.com/comic/10-25and, basically, Numair is indeed saying that he wants to broadcast in order to bring public pressure on the Council. 'They can stonewall the Cynn, he's only one person. But they can't stonewall everyone' -- not precise quote, but pretty close.
Ideally, I think, the Council's resistance would be part of the broadcast, in their own words. But Numair's speech on its own, with the information that the Council wouldn't even stay to hear it -- that might well have the desired effect.
Or, at least, something adjacent to the desired effect. Numair seems to think the public will just bring pressure on the Council, and the Council will then agree to form the interplanetary anti-slavery body which Numair thinks can do the job without starting a war. But what if the public throws the Council out entirely instead? Has Numair even considered that?
I do get the impression that he'd considered the possibility that the Council would walk out, though.