Hello. You have an Interesting question here .
I'm not a dermatologist but i can give you an advice. I understand that the person who wants to take Propecia is a teenager but i didn''t understand if is a female/male.
VERY IMPORTANT : If he/she lost his/her hair already at this age first need to see a specialist for some tests to find the main cause of the affection.
And i would totally say NO to this drug for Alopecia areata because even is good for your hair loss the side effects might be irreversable and influence quality of life by
having a decreased psychological well-being in terms of energy, social isolation and emotional reaction and a disturbed sex life compared with normals : Decreased Libido;Erectile Dysfunction ;Ejaculation Disorder (Decreased Volume of Ejaculate)
Read more:
http://www.drugs.com/sfx/propecia-side-effects.html#ixzz0vFgA6NHv
http://www.webmd.com/skin-problems-and-treatments/hair-loss/hair-loss-treatments-men