That seems a little bit too niche. I know that many people would be interested in that, but I for one, though interested in archery, simply don’t have the patience to learn the many skills necessary to make a bow. The smithing mini-game seems to be more of a general thing: sharpening blades e.t.c. Things anyone could understand.
I would guess, however, that you can make bows in the game. The first thing I thought of when I read the topic was a situation: you’re out in the wilderness without arms, you cut, shape and polish some branches quickly, snare a bird, et voila, a crude bow and arrow. That might work, at least as a main story quest.
As for testing them, there’s no point. The game won’t allow you to make a bad product. Everything will work as well as the stats (if there are any visible) allow it.