Rock climbing can broaden your shoulders, but it depends on how your body reacts to training.
I am normally pretty skinny, with not too much muscle. But, when I climb, I gain quite a bit of muscle mass, which makes it seem as if I have been lifting weights for a while. I very often get asked how I work out and how much weight I lift, which I don't, I just climb and at the most do body weight training such as pull-ups.
On the other hand, I have friends who climb and train almost exactly like me, who eat better also, but don't gain weight or muscle mass like I do.
So it really depends on your body and how it reacts to training. Some grow faster than others, some get stronger than others.