I do Parelli as well, and I can guarentee you that it will help your horse tons if you decide to do it. I found this quick little article Parelli wrote about horses that are one sided. It might give you a few ideas.
Because horses are prey animals they have bi-lateral vision. They see things out of each eye in distinct ways and when they feel unconfident or nervous they can overreact when you switch from one side to the other.
Humans tend to be creatures of habit and ritual, and one of the rituals that has evolved in modern horsemanship is to do things from the left side of the horse: approach from the left, put the halter on from the left, lead from the left, saddle from the left, bridle from the left mount from the left, dismount from the left, unsaddle from the left, unbridle from the left...get the picture? Unwittingly, what this does is cause the horse to become one-sided.
When we start with young horses in Parelli, we do everything from both sides so they do not become one sided. When we get mature horses that are already one-sided, we do more from the other side until it’s balanced out.
The more you can think like a horse the more you’ll understand what his needs are and how to balance them out naturally... mentally, emotionally and physically.