Does delaying the Fajr prayer until after sunrise, due to the assumption that there isn't enough time for both the Sunnah and Fajr prayers together, fall under the category of deliberate delay that expels one from the faith?

Scholars have differed regarding one who wakes up a short while before the prayer's time expires: should he prioritize the supererogatory (nafila) or the obligatory (fard) prayer? The more weighty opinion is that he should begin with the obligatory prayer and then make up the supererogatory one. There is another view, preferred by Sheikh Ibn Uthaymeen, may Allah have mercy on him, which states that he should begin with the supererogatory prayer, because the time for the obligatory prayer, for someone who was asleep, begins upon his waking up, based on the Prophet's (peace be upon him) saying: "Whoever sleeps through a prayer or forgets it, let him pray it when he remembers it; there is no expiation for it except that."