Yes, in the Tower the Black Ajah can easily kidnap another Aes Sedai, but there is no way for them to take the AS out of the tower or bring in Fades.
It would be harder to kidnap AS outside of the Tower. When the BA decided to reveal who 13 of them were it was for a major trap for the Dragon, not to catch one sister too early to be used in the Final Battle.
Turning people years before the Final Battle is too dangerous because they can’t hide who they are as well as the regular BA. Also once the Tower figures out people are being turned, the whole of the BA becomes at risk.