Tried it all out at LHR T2 today on an Avios redemption ticket.
OLCI could not attach my or Mrs. stifle's BA silver status to the booking. Desk agent was unwilling "we can't access it as it's not our booking". Lounge dragon tried and failed.
Nonetheless, all the entitlements (priority check in, fast track, lounge access, and group 1 boarding) were granted upon showing the BA app membership card.