TOGA Boy, in a perfect world, yes. However, this is not a perfect world and all sorts of medical cases slip through due to lack of passenger knowledge/ willingness to cooperate and/or failure of the ground staff to either notice or act accordingly. I suspect that in the future this will become more common due to on-line check-in and increasing ease of getting from the curbside to the airplane without the usual procedure of standing in line for a long time.
There have also been numerous cases where it has been hard to notice that a woman, due to her body shape, was pregnant.