I don't have exact knowledge of the case for AY, but if your BP says anything about Priority or fast track I assume they will let you in.
It is labelled something like VIP to the right of the other lanes. It is not guarded by BP scanner, just a guy and you ask him which line is Priority and he will send you in the right lane.
The Finnair app and webpages usually offers to sell the things that already are included in your ticket, that is their SOP. If you click through on trying to buy it, there is an error.