While it is true that the election of a Major Archbishop needs the confirmation by the Pope for it to be valid, the election of a Patriarch does not nor does it need papal recognition.
The Synod of Bishops of a patriarchal Church is endowed with competence to elect and to enthrone her Patriarch without further ado. He can immediately exercise his powers and authority, except (1) the convocation of the Synod of Bishops and (2) the ordination of Bishops while awaiting answer to his request for ecclesial communion with Pope.
Simultaneously or at a reasonable time after the enthronement, a Synodal letter must be sent to Rome and to all Eastern Catholic Churches informing the election and enthronement of the Patriarch. Then, the “new patriarch must as soon as possible request ecclesiastical communion from the Roman Pontiff by means of a letter signed in his own hand.” (Cf. Canon 76, CCEO).
Thus, the election and enthronement of the Patriarch stays no matter what. However, if the new Patriarch does not send his request for ecclesiastical communion with the Pope, or if the Pope does not grant ecclesiastical communion, the Patriarchal Church remains not in communion with Rome.