It's a nice theory, but falls to pieces in say traditionally Catholic Ireland (history of powerful temperance movements also) and a cultural approach to alcohol which is if anything even more damaging than Britain's.
Ireland is a temperance culture as well (not surprisingly). Protestantism is not a necessary factor here, it's just that historically temperance cultures have tended to appear in Protestant countries, along with pietistic movements. I don't know enough about this to say whether religion has played a major role or if it's just a coincidence.