This question involves a lot of different permutations.
First question is this varies from jurisdiction to jurisdiction. EMTs are licensed under the medical direction of a doctor connected to the local emergency room. Then the state has it's requirements and guidelines. This determines when an EMT gets to call someone.
The starting point is the severity of the injuries. This has to be combined with the length of extrication. If we arrived on the scene and the person had no pulse, pupils fixed and dilated, and significant injuries, and we we're looking at an hour or more for extrication, we'd call it, after talking with the ED.
If there is any sign of life, we'd transport, even if we knew they were going to get called at the hospital. We had one patient that had so many leaks we used up all of our IV bags during the extrication and transport. CPR all the way and by the time we got to the hospital, his blood was a very pale pink.
One criteria for calling patients is the ten minute window for brain death. No CPR and no pulse for more than ten minutes and the brain is dead. Shorter periods will cause damage, the longer the more damage. You can't do CPR with a seated person very effectively. Also, as Tsu said, with multiple victims, you do triage and depending upon resources, you might call someone because by the time you're able to deal with them, they're going to be dead.
Once someone is declared dead, then the question becomes whether the police feel there is a crime scene involved. If the police determine it's a crime scene, then the fire department would have to wait until they got done with their investigation. And a lot of wrecks involving a dead body are crime scenes in which one or more of the drivers will be charged with a crime such as DWI, speeding, reckless operation which can result in a charge of negligent homicide.
If the accident is a crime scene, then the body has to go in for an autopsy. You can't tell whether the person had a heart attack or stroke shortly before the accident, and for another driver to be convicted of negligent homicide, the victim has to have died from the accident.
If the prosecutor, the medical examiner, and the police agree that no crime has been committed, the body can go directly to the funeral home.
Remember that depending upon the area, EMTs can be separate from anything else, part of the fire department, or part of the police department.
I would talk with the rescue squad for where you want to stage your accident. I was a EMT/firefighter on a volunteer squad for many years.
Best of luck,
Jim Clark-Dawe