As a small experiment, I drew my left hand with my right hand and my right hand with my left.
I definitely noticed the difference!
Despite the noticeable differences visually, I could tell that my state of mind was in fact different for each drawing. When I used my right hand, I was more rushed, My lines (although neater) where less accurate and I actually made more mistakes than when using my left hand!
When using my left hand, I found it much more easy to understand the shapes and both the proportions and general shape of the image was far more accurate than with my right hand!
I can tell, without a doubt, that there is definitely a neurological change when switching from right handed drawing to left handed drawing. I may explore this deeper as part of the brief.