My Grimoire is relatively high (4725 which obviously is not as high as yours) and I voted no.
Grimoire is more about time than skill.
I class myself as merely ok at the game. (I have completed hard raids many times but there is no way I am ever getting to the Lighthouse).
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But for pvp I said something different. There are people in my friends list that have high Grimoire but I can't play trails with becasue they are not good at PvP. You can see that in their Grimoire. But they will always be my go to man for the raid.