Does the Element materia do more damage based on the level of the materia it's paired with?

Here's the situation: you pair an Element materia with another materia with an elemental type (say, for example, Fire). The question is: does it make any difference whatsoever if the Fire materia has tons of AP or is brand new? If the Fire materia is capable of casting Fire 3, does that boost the weapon damage granted by the Element materia? Or is it irrelevant?

Solution 1:

No.

Element materia linked to a materia with element type only gives you a damage multiplier against monsters with elemental affinities.

If the monster is weak against the linked materia, you do 2x dmg. If the enemies are resistant to the element, your attack can do either half dmg, no dmg, or heal the enemy.

From what I can remember and what I have found through searches, the damage provided by the combination does not scale with either the level of the Element materia or the materia it is paired with.