I shot my first deer ever left handed. And for many years after that, it was the only time I had every shot left handed. I attempted to do it again last year as I had a buck come up on the right side of my blind while I was sitting in a camp chair. I couldn't spin around so I shifted the rifle but I think he heard or saw me and ran. This year I have a bucket with a rotating lid so I can spin around at will.
I guess it depends on the situation, If I thought I could move to take a right-handed shot, I would do it. If I thought I couldn't and couldn't wait until I could, I would take a left handed shot. With a scope, shooting with the opposite hand at close range isn't that hard.