In any case, we know she was a member of the SC, as Egwene told Sheriam herself in front of the Hall Verin identified her as one.

She did think of Delana in the same scene without mentionning it was a pity a leader of the BA had fled, so I would guess your guess about her is wrong.

The Black Ajah Hunters could not really use the sign (which they must have gotten from Talene). It's rather obviously a special sign, to be used under orders or in specific circumstances (danger, for instance). Identifying themselves as BA in front of a Black wouldn't exactly have been wise in their position. They would have needed to arrest her if the bait worked... it sounds like a good way to blunder and end up attracting attention. Their methods of luring in the basement sisters they had good suspicions about sounded like the best one.