No. The law of the Church is consistent on this across all rites.
It is possible for the child to be baptized into the Latin Rite if both parents agree. Otherwise the child is to be enrolled in the Rite of the father. In this case, that is one and the same thing.
Can. 111 §1. Through the reception of baptism, the child of parents who belong to the Latin Church is enrolled in it, or, if one or the other does not belong to it, both parents have chosen by mutual agreement to have the offspring baptized in the Latin Church. If there is no mutual agreement, however, the child is enrolled in the ritual Church to which the father belongs.
- Anyone to be baptized who has completed the fourteenth year of age can freely choose to be baptized in the Latin Church or in another ritual Church sui iuris; in that case, the person belongs to the Church which he or she has chosen.
Can. 112 §1. After the reception of baptism, the following are enrolled in another ritual Church sui iuris:
1/ a person who has obtained permission from the Apostolic See;
2/ a spouse who, at the time of or during marriage, has declared that he or she is transferring to the ritual Church sui iuris of the other spouse; when the marriage has ended, however, the person can freely return to the Latin Church;
3/ before the completion of the fourteenth year of age, the children of those mentioned in nn. 1 and 2 as well as, in a mixed marriage, the children of the Catholic party who has legitimately transferred to another ritual Church; on completion of their fourteenth year, however, they can return to the Latin Church.
§2. The practice, however prolonged, of receiving the sacraments according to the rite of another ritual Church sui iuris does not entail enrollment in that Church.
**1. By virtue of baptism, a child who has not yet completed his fourteenth year of age is enrolled in the Church sui iuris of the Catholic father; or the Church sui iuris of the mother if only the mother is Catholic or if both parents by agreement freely request it, with due regard for particular law established by the Apostolic See. **
- If the child who has not yet completed his fourteenth year is: (1) born of an unwed mother, he is enrolled in the Church sui iuris to which the mother belongs; (2) born of unknown parents, he is to be enrolled in the Church sui iuris of those in whose care he has been legitimately committed are enrolled; if it is a case of an adoptive father and mother, 1 should be applied; (3) born of non-baptized parents, the child is to be a member of the Church sui iuris of the one who is responsible for his education in the Catholic faith.