If one who misses the two rak’ahs sunnah before the Fajr prayer may be allowed to offer them after the prayer, before the sun rises based on the following Ahadith:
Qays ibn ‘Amr who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) came out when the iqaamah for prayer had been given, and I prayed Fajr with him, then the Prophet (peace and blessings of Allaah be upon him) finished and found me praying. He said, ‘Take it easy, O Qays. Two prayers together?” I said, “O Messenger of Allaah, I did not pray the two rak’ahs before Fajr” He said, “No, then.” [narrated by Tirmidhi]
According to the version narrated by Abu Dawood, the Messenger of Allaah (peace and blessings of Allaah be upon him) remained silent.
According to Shariah , if one performed the Fajr Salaah without having read the Sunnats, there is no Qadha for the Sunnats. However, if the Sunnats of Fajr were missed toghther with the Fardh, then one may read the Sunnats when making Qadha after sunrise. The Hadith that you have qouted also indicates that one should not read the Sunnats if they have been missed.
and Allah Ta’ala Knows Best
Mufti Ebrahim Desai