They might not be recognized by any outside force, but it should be easy for a traitor inside the WC to point anyone who is asking questions to those regarded as troublemakers.
Then again, they are human, they are wizards, as far as anyone is concerned, they are WC. Of course some supernatural forces might learn about their "condition" and try to take advantage of it, but without any reason to think otherwise, they could be regarded as members.
On the other hand, why should they completely reject the council? They could just be members on paper, simple as that.
The question, I think, should be, do you and your players want to play a WC centric game or not. If you don't want the council involved at all, just don't involve the council (or rather: don't involve them more). Just let them be gone and let their characters develop the way they seem fit. If the players specifically want to act against the council, then make that part of the plot.
I think it was PG, where Charity talks about the warden that came to the cult she was in. The only thing he did was to tell them the laws of magic and then he was on his way. You could do the same, maybe give them a contact "if they change their minds". If afterwards they chose to break the laws of magic, that should still have consequences of course.