I don't think it is?If we are a Primal, none of the Hydaelyn stuff would make sense. Also, crystals don't vanish en masse as we walk around.
I think the distinction is that Eikons and Elder Primals like the Warring Triad, Odin, and Bahamut don't need crystals to sustain themselves, and may not need crystals to summon them either. Phoenix definitely didn't need crystals, but only a lot of prayer.
But yeah, it's still headcanon at this point though.