I don't think so. Anaphylactic shock often includes having the lungs filled with fluid. It happens very quickly. A student in my immunology class visited the vivarium as preparation for selecting a rabbit for creating antibodies to beef serum albumin. The student was completely unaware of an allergy to rabbits. The class observed a horrible example of anaphylactic shock first hand.
Thanks for the clarification. I had thought that the problem was primarily with the throat constriction.