Was this sort of case addressed in sacramental theology before V2? It’s the same thing as saying: what would happen if there is a Mass going on where everyone thinks the priest is a valid priest offering it, but in actual fact he is NOT a valid priest but nobody knows.
What happens to the faithful? Do they receive zero graces? Less? The same? Of course it’s not their fault at all.
Same with confession.
I have to think that they would, indeed, receive graces, due to the disposition of their hearts, not sacramental graces, but God's grace is not confined to the sacraments. What kind of grace it is, that's outside my pay grade.
As to the OP, I have noticed "a certain something", can't quite put my finger on it, but it's there. I struggle for words here (a problem I don't often have), but there is a certain presence, an etherealness, about both SSPX
and FSSP priests, whereas priests outside of that framework often seem more "down-to-earth". One priest I knew, not of the SSPX but associated with them (at the time), was one of the most approachable, friendliest, common men you will ever meet, the kind of guy you could sit down and have a beer with, yet totally traditional and orthodox in the Faith. It might be a formation issue.