I played 9 full holes once left-handed...as I play right-handed normally. It was a round with beginner friends who I didn't want to always be waiting for.
I shot a 56 (+21) and I was pretty happy with that. I could hit the ball pretty decently, but no further than about 175 yards with a driver. I did find the short game (no bunker shots) to be relatively easy to get used to...I didn't putt half bad.
Playing baseball growing up, I toyed with LH hitting at full speed in practice, and my hitting style was similar...high contact with little power. Never tried it in a game though...I wasn't good enough hitting from the (normal) right side.
There are many golfers proficient from both sides...we had an asst. pro who couldn't get to scratch from his natural left side, switched, and got to plus from the right. I also have heard that Vijay (among others) would be a low single-digit from the other side.