All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
If the person to whom you referred in the question marries that girl and the marriage contract fulfils all the conditions of a correct marriage contract which are mentioned in Fatwa 92335, then the marriage contract is valid and announcing the marriage is not a condition for its validity. However, it is desirable to publicly announce the marriage as the Prophet said: "Make the marriage public." [Ahmad & Ibn Hibbaan].
Nonetheless, a man who marries a woman, without the consent of both his parents or the consent of one of them, especially if they have a sound reason for refusing, may be sinful even if the marriage contract is valid because it is an obligation to obey the parents but it is not an obligation to marry a specific woman. Indeed, there are many women and he may marry any other woman.
For more benefit on the ruling of marrying without the consent of parents, please refer to Fataawa 92340, 89650and 83379.
Allaah Knows best.