Well your mystic wont be able to do most of the quests given out in Freeport, and the necro wont be able to do most of the quests qiven out in Qeynos, however most quests in the game (including most of the ones in Commonlands and Antonica) can be done by both factions.
There are some along the way that only one side can do (theres a load in Lesser Fay that evil people cant do for instance, grumble grumble grumble - mutters the Freeportian ratonga), but after the first 10 levels in the game most quests can be done by both factions.
But yes, assuming your on a PvE server you can happily quest together.