I agree with the idea of this. I've definitely had this happen, especially in intercepted ufo missions when you tend to be started within firing range of a couple guys. In lieu of changing the starting positions for the maps, I think I'd vote to just allow Electro lasers to shock to life.
Giving some kind of unconscious mode would be rather complicated but possibly the most realistic.
Whereas shocking dead soldiers to life is possibly less realistic.
Depends on what you're going for, realism wise.
A Defibrillator/Adrenaline Kit or Upgraded 6 box MedKit to allow reviving dead soldiers could be both technically easy And somewhat realistic.
On the debated suggestion of jon_dArc and CheeseshireCat I'd say that I like a combination of their suggestions the best.
The Unconscious/dying status has a 2 turn time limit to get him medicated/stabilized, and then the soldier is still down for the match and has to heal in a hospital.
Either shocking to life or medkits for reviving.
IMHO, I think the penalty is quite balanced with the benefit of saving the soldier and realism.
Not only do you have to waste a medkit, be down a soldier, and waste 20 TU. You also have to look forward to a long recovery in the hospital(which already seems long for even half health).
Indeed, the penalty is severe enough that I would definitely not spend the medkit on just anybody. I wouldn't really be tempted to restart the mission.
Or maybe you could just use electro lasers to shock people into low health or maybe dying status?