Quick thinking will save you from dying due to self-inflicted damage, but the pool of backup-health at your disposal is limited by the energy you carry, and most weapons that self inflict damage deal much more than your maximum capacity modded. E.G. Taking a massive amount of self-damage from your own Penta rounds will drain your shields first, then your health to 2, and any leftover damage carries over to be stopped by Quick Thinking.
As of Update 11.1.0, Quick Thinking will keep your health at 2 and use your remaining energy to keep you alive from incoming damage. The efficiency will go up with the mod's level.
Rage will still grant you energy taken to your health until you reach 2 hp (filling up your energy pool), at which point the mod will stop giving energy (as you are not taking health damage) and Quick Thinking will take over, using your Energy pool as a buffer against your remaining 2 hp. Once losing energy, you will go beyond the 2 hp and die.
Damage to energy is affected by armor, and all damage numbers seem to be rounded up (needs further testing).