It's entirely appropriate to stick the lawbreaker stunts on the character, to represent the tainted use of magic. This has NOTHING to do with the white council. Using magic in a bad way affects your self concept, your soul. Even if your magic comes from an external source.
I'd slap the -2 lawbreaker on the character at creation, so that you represent a past of doing this, and so that the player never has to worry about going negative refresh and becoming an NPC.
Now, for the white council, we can say that if you are under a different signatory, they aren't supposed to come for you. But that doesn't mean that if you are under a different SPONSOR, they WON'T come for you. Example: Necromancers. Kemmler obviously didn't sign the accords, as the white council killed him, and attempts to kill anyone that magic sponsors. So, basically, you need to clarify if Death popped over and signed the Accords, and if everyone else would let Death sign.
In my game, for instance, the Church is NOT a signatory, and 2 PCs work for the church. One of the PCs is an emissary for a dragon, who IS a signer. Another is an emissary of Tiamat (who is NOT a dragon, but more of an undead primal chaos chimera being), who is NOT a signer. Both emissaries have lawbreaker, but one has to worry about the council. Meanwhile, the holy PCS engage any evil they want, without breaking the accords, but with knowledge that the accords don't protect them in any fashion.