The game should always add promo cards if you have them. There isn't any minimum AD check.
Easiest way to verify this is to start a B scenario and go check out the vault. Those are all the cards that are available for play that session. All the Promo cards you possess should be visible alongside B-Deck and C-Deck (if you have it).
Well, that is wrong. This is what Rise of the Runelords FAQ have to say about adding Promo cards to the box ...
Good catch. Paizo.com seems to be hard down right now, but I believe you're right.
When I said "the game should" it was an observation/analysis of how the App behaves. I wasn't speaking for the whole body of rules and errata that makes up the Pathfinder ACG universe.
Should the app check when to add promo cards? FAQs say probably. Does it? No, it does not. Promos are currently found in B onward.
Unless a dev is willing to chime in, it is hard to tell if this is another minor deviation from the Pathfinder ACG body of rules, or if they just missed the errata.