I would have to say that either side would become stronger if trained to do so. I believe it has to do more with the coordination and flow which is heightened with shooting with the dominant side.
Aiming is done with the eyes while having the ability to adjust the bow accordingly while keeping the proper form.
The trick is getting the arrow to go where you are aiming. I think there are a lot of people who aim correctly, but because of flaws in form, the arrow does not go where the person is aiming.
Personally, I am left handed. I write and eat with my left hand, so people label me left handed. However, my dominant back, arm, and shoulder are on my right side and most of my athletic activity takes place on my right side including drawing my bow.
Not saying this is the way it has to be for everyone, just sharing my experience.