Aline Gädeke

Can Aline Gädeke use her special to unlock after another non-anarch vampire successfully performs the "become anarch" action?

Didn't you just answered on your question? 'another non-anarch vampire successfully performs the "become anarch" action'

She cannot.

Aline's special checks the sect of the acting vampire at the resolution of the action.

At the resolution of the become-Anarch, cardless action the vampire is an Anarch, who completed a successful action. She can use her special.

Similarly, if an Anarch vampire equips with Write of Acceptance, at resolution that vampire is no longer an Anarch and she cannot use her special.

The key question and precedent setter here is if an action is considered performed by a vampire with the sect/clan belonging that they had at the beginning or the end of the action (or potentially both).

This ruling would affect Aline Gädeke´s special in regards to both actions making a vampire Anarch and actions making a vampire non-Anarch

Ankha´s decision and explanation will be interesting.

My bet is she can't.
Non-anarchs perform this action and they become anarchs if this action is successful.

That is all true but maybe Aline does not care, because she says "after". The action ends, Aline takes a look and sees an Anarch that performed a successful action. Voila, now she can pay 1 blood to unlock, why not...