Were there units set up specifically for this task?
What about wounded that were missing but not located yet? I heard anecdotally that the French philosopher Gabriel Marcel was involved with Information Services and had an affinity for finding missing soldiers.
As a follow-up, were there specific evacuation units during later wars like WW2 or the Vietnam war?
In WWII the US Army had a system set up that ensured that wounded soldiers were located quickly and moved to the rear for treatment, which gave them a better shot at surviving their wounds
I. Each man carried with him an M1942 first aid pouch that contained a sterile Carlisle bandage and a packet of sulfonamide powder, which could be sprinkled on open wounds to avert infection
II. Each infantry regiment had a medical detachment, with three sections for each of the battalions that provided the ubiquitous aid man or medic (in military parlance Technician, Surgical, Specification Serial Number 861) for each rifle platoon in the rifle companies, and machine gun or mortar platoon of the heavy weapons companies (the weapons platoons of the rifle companies oddly weren't allotted a medic). Each battalion section also had litter bearers that assisted the surgical technicians in moving the wounded men from the field to the battalion aid station. Each infantry regiment also had its own aid station; this station was mainly used for the regiment's rear-area personnel. Frontline soldiers didn’t normally go here.
III. If the soldier was more seriously injured and required more specialized treatment, he went to the division's aid station, administered by the organic Medical Battalion. Each Medical Battalion had three collecting companies (with Dodge WC ambulances, this one number 7 of the 2nd Armored Division's 48th Armored Medical Battalion) that moved casualties from the battalion or regimental aid station up to the divisional level. The two platoons of the clearing company assessed soldiers’ conditions, treated and released them back to their unit, or stabilized and prepared them for transport to a semi-permanent general hospital, where more extensive surgery could be performed.
IIIa. At this point, the soldier usually passed through an evacuation hospital. Evacuation hospitals served many functions. They sorted casualties received from divisional clearing companies that were slated for transport to general hospitals further to the rear, and also worked in reverse, sending men who recovered there, back to their units. Sometimes, men passed through an evacuation hospital on the way back to their unit after leaving a general hospital.
IV. The semi-permanent general hospitals were located well behind the front lines (several hundred miles in some cases, although often in liberated enemy territory) so patients often required air transport to be moved there. General hospitals had the most advanced medical equipment in-theater, and most major surgical procedures were performed here. If a soldier recovered within a reasonable amount of time (usually about 180 days) he would be sent back to his original unit (very rare, but policy changed later in the war to make this more common) or be sent to a convalescent camp, and then a replacement center for eventual placement in a new unit.
V. If a soldier was severely injured or disabled, (his injuries exceeded the treatment options available at the general hospital) he would pass through the general hospital after assessment and be returned to the Zone of the Interior as quickly as possible to receive specialized or long-term care, after which he would be returned to limited light (desk) duty or discharged.
Sources:
US Army Medical Department Office of Medical History