As far as I know, Azrael is one of the angels of death, who has the duty to collect the souls of those who died. However, I don't know if he has such a "deathly touch". Where do you got that information from?
A quick search reveals there is a spell on this site which speaks of Azrael's touch, but I can assure you no spell will truly grant a mortal the ability to reap souls. How such a spell received such a high rating without any one noticing it in order to correct it is beyond me but I digress. Azrael is said to record the birth and deaths of mortals though whether he actually kills probably varies upon beliefs. Typically in Christian beliefs you might deem such a being to take these actions, but only under orders as angels aren't generally depicted as having free will so he couldn't go around killing indiscriminately.
I don't think Azrael touch people and people just die. He just deliver the soul of the Dead to where the place of soul belongs. He's the reaper but not like the Death reaper that appears in Death Note anime where he can kill people randomly. As far as I know, his mission is to grab the soul when people are going to die, including those who experiences the near-death experience. Azrael actually trying to grab the soul from the body when NDE happens as people struggle to survive and try to be still awake.
If NDE happens longer, it become more difficult.
But in some case people can survive even if they are in coma condition for a week,,