Be honest with your natural ambidextrous tendencies. Can you shoot a basketball OK left handed? Can you handle a pen decently left handed? I think that is a indicator of how quickly you could pick it up.
Will you be as good as you were right handed? Nope.
Could you get to the point of throwing strikes and being somewhat effective? Maybe.
I for one can't do much at all with my left hand, so I know this would never be an option for me. I'm severely right hand dominant.