Generally not. The most common use of alert bracelets are to alert emergency medical personnel to treatments that, if given in a situation when you can't provide input to your care, will result in more harm than good. A classic example is penicillin allergy, in which you would not want someone to give you penicillin if you were unconscious. This type of situations usually doesn't apply to asthma and hay fever.
Possibly... If it is possible to be in a situation where emergent care may be needed at a time where nobody can speak for you and provide healthcare workers with information which may be life-saving, then an emergency alert bracelet/pendant should be worn. Example would include a child with anaphylactic peanut allergy. Severe life-threatening asthma is another example where this could be life-saving.