I have actually tried experimenting this theory in the low lvl dungeon Sashtasia with unique gear in one instance and then ran it again with the highest gear I had as WHM (34) and I can safely say that my stats were better in the relevent unique gear for that lvl dungeon due to the fact that the gear was rated higher than my actual level sync.

That being the case, I see no reason why this would differ in higher lvl instances.... so may be worth keeping that lower lvl unique gear if you want to have the best for re-running lower instances or even fates.