You're free, whether they know it or not; whether they struggle against it or not.
The story is that the local bishop and stake president have to be informed ... I guess because these people sometimes really do care and can out of good intentions may make contact even after you asked for officially no contact.
For me, it took a week or so before we got a form letter from SLC saying they got our letter and were forwarding it to the locals. In about a month or so the bishop dropped off the letter.
Technically, the moment you say, "I quit" they have no power over you. If they call you to church court you should have legal recourse. Others know more about this that I do. My quitting was pretty smooth.
I resigned from the Church of THE Jesus Christ of the Latter Day Saints (Feb 2011)
"For nothing is secret, that shall not be made manifest; neither any thing hid, that shall not be known and come abroad." - Luke 8:17