Up until the Vietnam era, Military medics were basically just there to bandage you and stop hemorrhaging. THen you were triaged at a rear area before either being shipped out for more advanced care or put back into action. Back then, each Infantry Battalion would have it's own surgeon who would actually be very close to the front lines. Several Surgeons were killed during the Normandy landings for instance.
With the advent of air medevac in the 1950's and '60's, the frontline medic/corpsman began to get more extensive training in stabilization and could do more in the way of actual treatment. It was during Vietnam that our casualty rates started to drop dramatically due mostly to the ability of medics on the ground being able to call in a bird and get a critical casualty to a CASH/MASH Unit within the golden hour.
Today, our basic medic is an EMT with almost Paramedic level protocols. He can put in a chest tube, intubate, decompress a pneumo, and give narcotics all while under fire and without medical direction. It's because of this that over 90% of traumatic injuries on the battlefield in Iraq and afghanistan survive.
So to answer your question, no, a WWII medic was not as well trained as a modern EMT but was still your best friend when you got hurt.