Narrated ‘Aisha and Um Salama (radiallaahu `anhumaa):
At times Allah’s Apostle (sallallaahu `alayhi wasallam) used to get up in the morning in the state of Janaba after having sexual relations with his wives. He would then take a bath and fast.
The fast of one who has intercourse with his wife at night and wakes up in the morning in a state of junub is still valid, as is the fast of one who becomes junub in his sleep, whether at night or during the day. There is nothing wrong with delaying ghusl until just before dawn. Rather fasting is invalidated by having intercourse during the day in Ramadaan, from just before dawn until after sunset.
Fataawa al-Lajnah al-Daa’imah, 10/327
Usually what happens is, being in the state of janaabah, people tend to delay ghusl (due to embarrassment or other reasons) and miss Fajr. This is not acceptable. One must make sure to pray on time as well.