Do Gelb and Bartim eventually denounce Rand as a Darkfriend?

Halfway through The Eye of the World, the first novel in the Wheel of Time saga, Rand’s little troupe find themselves in Whitebridge and

Rand just stood tall enough to see over the wall, then ducked back down again with a sinking feeling in his stomach. Floran Gelb sat on the other wide of the wall, at the table in the back with the two men who had been there when they came in. They were laughing at him, but they were listening.

…

The laughter erupted on the other side of the wall, broken again by Gelb, trying loudly to convince the two men he was telling the truth.

For a long time they leaned against the wall, not talking. Rand was not sure how long they waited. A few minutes, probably, but it felt like an hour, waiting for Thom to come back, waiting for Gelb and Bartim to open the windows and denounce them as Darkfriends … [and] Whitebridge roiled like a kicked anthill.

Does Gelb or Bartim eventually denounce Rand and his friends as Darkfriends?