I asked my SSPX priests weeks after we were married what he did with the docuмents and he told me they are sent to the diocese and to the headquarters in Kansas City.
Just because they are sent to the diocese does not mean they are recorded in the diocese records.
People forget... the sacrament of matrimony is not given by the priest. It is given by the bride to the groom and vice versa. The priest is only the witness in the eyes of God.
So whether or not your marriage is "legal" in the eyes of the Church does not matter to God. What matters to God is your state of mind during your wedding and whether or not you received the sacrament or gave it.
All those SSPXers who are getting annulments are in for a rude awakening when they die.