A witness from the Church is necessary for the marriage to be valid (distinguished from licit) in the Church.

The Church accepts that a couple is married, but if they weren't married under the witness of the Catholic Church, their marriage must be validated in order for them to receive the sacraments. 

Of course, the Church's impetus is "union"...not just conjugal union, but larger communion with the Church.  Most Catholics don't really "get" the fuller meaning of union/communion.  They just don't get it.

Our union with God is manifested for instance in whether we sin, whether we obey the will of God, whether we are validly married, etc.  Even when we give money...agreeing to support the church is an act of union.  And that's why such support is one of the 6 precepts of the Church.