Can the Church Celebrate Secret Marriages?

Would two people in the witness protection programme, who know each other's real identities, be able to get married in a canonically valid manner? There is more than one way of handling this canonically. The code of canon law does contain provisions for marriages that are celebrated secretly. And that includes the ability to do secret checks on the things that normally have to be checked before a marriage is celebrated. So it would be possible for the people in the Witness Protection programme to have the church secretly investigate and make sure they're not currently married to anybody elsend. It doesn't happen very often, because most people who are getting married are planning on living a normal conjugal life. Ah, but