Data point:
Twice now when putting my wife's US FFN onto a BA res (she is the only one with a US cc), we both got the ability to bring a bag for free, but only her boarding pass had Zone 2 boarding, mine had a later boarding. Wasn't a problem as I just put her boarding pass on top of mine and we both go on at Zone 2, but just letting you know.
Also, the beginning of this thread (and the title) implies that you get benefits just by the fact that you booked with Avios - seemingly without requiring the switch of the FFN.