Annulment is the recognition of reality, no? A marriage is de facto not a marriage even before the church recognizes it is not. Those who know that they do not have a marriage or did not make a valid marriage, do not sin thereby and I do not know anyone who teaches that they do. The forms and forums only to ensure your conscience. They do not change the state of reality.
Or course they sin. They sin by lying to each other, to the witness (e.g. priest) and to God. They continue to sin by fornicating if they think they're not in a valid marriage.