I can see a way that the Mormon church goes down that path, but the proselytize is typically a one on one nature by going on a mission rather than billboards. It does happen I've seen Ads for the LDS Church before (you'll never see one for Mormons).

I think the "moral duty" portion comes in on an individual basis within the church so it's a character building exercise to spread the faith as well as a moral duty. I can definitely see what you mean though there could easily be some interpretations that lead to Ads.