So in a non-canonical sense, someone can be privately married to God? (I’m not refering to anything others would have to recognize as such.)
I am not fitted to discuss such terms. Though one can note that the Church is the Bride of Christ…we are all his.
As to the formal Consecrated Virgins or Widows this is what the Catechism notes:
Consecrated virgins and widows
922 From apostolic times Christian virgins461 and widows,462 called by the Lord to cling only to him with greater freedom of heart, body, and spirit, have decided with the Church’s approval to live in the respective status of virginity or perpetual chastity "for the sake of the Kingdom of heaven."463
923 "Virgins who, committed to the holy plan of following Christ more closely, are consecrated to God by the diocesan bishop according to the approved liturgical rite, are betrothed mystically to Christ, the Son of God, and are dedicated to the service of the Church."464 By this solemn rite (Consecratio virginum), the virgin is "constituted . . . a sacred person, a transcendent sign of the Church’s love for Christ, and an eschatological image of this heavenly Bride of Christ and of the life to come."465
924 “As with other forms of consecrated life,” the order of virgins establishes the woman living in the world (or the nun) in prayer, penance, service of her brethren, and apostolic activity, according to the state of life and spiritual gifts given to her.466 Consecrated virgins can form themselves into associations to observe their commitment more faithfully.467
Now if someone made a private vow of say celibate chastity --that is yes a further consecration to God (of one who is already consecrated to him by the most wonderful consecration of Baptism). One that brings with it greater merit and greater moral responsibility via the virtue of religion.