No. Just as it doesn't cost extra MP to hit every enemy when linked to an All materia, it doesn't cost extra to replicate the spell with Quadra Magic. The effect of each of the four castings is weaker, but since it occurs four times, the overall damage is much higher. W-Magic does require you to pay for both spells, but again, Quadra Magic incurs no extra MP cost. Ultimately, you would get eight spells for the price of two, so to speak.