To what extent is the Sheikh's statement correct that a sleeping person is like a dead person, and that whoever cannot resist sleep to perform acts of obedience will not be able to say "La ilaha illa Allah (There is no god but Allah)" in the throes of death?

The assertion that not resisting sleep to perform acts of obedience implies an inability to pronounce the Shahada at the time of death has no basis or evidence. Uttering the Shahada at death is a sign of a good end, but failing to pronounce it does not necessarily mean a bad end. While a person’s life usually concludes upon what they were accustomed to, their ultimate fate is in Allah’s hands. He may grant a good end to someone who lived in disbelief, which is why the Hadith (definition) states: "Indeed, a man may perform the deeds of the people of Hellfire… then the decree overtakes him, and he performs the deeds of the people of Paradise and enters Paradise…"