No. Adrenaline/Epinephrine is produced naturally in humans by adrenal glands against "flight and fright" reaction. Any stress reaction reaction would thus initiate an uncontrolled positive feedback loop if we were to be anaphylactic to adrenaline. Situations of flight and fright would lead to release of adrenaline which would lead to collapse. This in turn would trigger release of more adrenaline.
