Is it possible to survive with a hypersensitivity/allergy to adrenaline?

Not possible. The reaction to adrenaline is more likely from the expected side effects from it and not an allergic one. However it is theoretically possible that one may have an allergic reaction to one of the additives in the solution.
Unlikely. Adrenalin is naturally made by the body and released during the "fight or flight response." Adrenalin is the medication of choice for treating severe allergic reactions. If a person had an adverse reaction to Epipen (epinephrine) that contains adrenalin, it is likely that it was not related to the adrenalin, but possibly an additive.