I broke my right arm (I'm right handed) while playing soccer when I was a Senior in HS. I was in a cast for 6 months and had to do everything left-handed (This was before I played DG). Now, 7 years later, I think having to use my left-hand for 6 months has aided me in throwing off-hand. I play rounds lefty from time to time and my drives are definitely there. My putting suffers, though. I think if I drove lefty and threw upshots/putted righty my rounds would be almost as good as all righty.
I think off-hand just comes down to forcing yourself to practice it and eventually utilizing it in rounds.