No, Church law requires that any marriage they perform be recognized in civil law. Please note that the "blessing service" mentioned below does not refer to a Catholic Church.
Answer As an additional answer, in case the questioner is considering looking elsewhere other than the Catholic Church I know of no church whether Catholic or not that will perform such a service. One cannot be married in Church unless the marriage is also a legal occasion and recognised in civil law. However some denominations will provide a 'blessing' service but not a marriage.