As of Update 11.1.0, Quick Thinking will keep your minimum health at exactly 2 HP 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.
While under the effects of Quick Thinking (2 HP and losing energy instead), strong hits against you will cause a 'Stagger' effect, briefly causing your warframe to stumble in place. Be wary, as repeated strong hits can effectively "stagger-lock" you in place until you die. Weak hits against you will not induce this effect.