As far as I know ther 'magic' is from mind and is originated from the far realm and has nothing to do with the weaved in fact that is why even Ao couldn't do much about the spell-plague. "Since the Spellplague was born from the defiling powers from the Far Realm, a plane that existed outside of Realmspace, not even Lord Ao had the power to stop it once it started.[8]" http://forgottenrealms.wikia.com/wiki/Spellplague
And as far as I can remember wizards and such utilize weave while performing spells, or when they dispel something-Even the anti-magic zone itself is described as a zone which weave doesn't exist in..So I doubt it would have any effect on a mystic from a lore perspective as their powers drive from their minds rather than interacting with the weave.