According to the article cited by @rosends a person who is sleeping maybe allowed to be counted in the Minyan with regards to Chazaras Hashatz. In that same article he notes: "Regarding one who is sleeping, we may not be lenient with more than one, Mishnah Berurah 55:32.)". It is a leniency to allow the Chazaras Hashatz to begin the repetition if only one person is sleeping.
However, a person who is sleeping is 1/60th dead, and is in no-way competent. Would one be rewarded for potentially not doing an aveirah or doing any of the 365 negative commandments because he is asleep? I would think not. A negative commandment requires a positive choice to do so. Being asleep hardly qualifies as being in a state of competency for being rewarded for mitzvos.
It is well-known that the effects of the day on a person's mental state can have a positive/negative affect on his subconscious state. For example, seeing a snake would possibly lead a person to dream about snakes (assuming this would affect him deeply). It is therefore more important to focus on one's day to ensure that Torah and mitzvos affect him deeply so that they would have a positive affect on his neshama.
I would be very careful about earphones in one's head while one sleeps. A person who tosses and turns (which is very common) could easily be strangled by the wires.
If there is strong medical evidence to suggest that listening to Torah while one sleeps is effective, then it would make sense to listen specifically to the Chumash or Tanakh being leined. Since this area of Torah imparts kedusha, even if one does not understand it, it may be worthwhile. However, listening to Torah that requires understanding sounds to me like a pointless exercise since you need to be conscious to understand it.