I was strictly a right handed shooter, and then had an injury to my right eye. The sight was not good in that eye, and shooting was out. My left eye naturally became my dominant eye, and I started shooting lefty.
Fast forward eight years, and I had cataract surgery which brought the right eye back to 20/50. Plenty good enough to shoot right handed again.
Knowing then, what I know now, I would have started shooting with both hands without the injury. It is just plain fun, and it does balance out your muscles, and heck, it was a great excuse to buy more bows for the other side.
It is a fun challenge, and if you were thinking about it; my advice is go for it.