Yes, I have done DC on a rainy day. When we went June 2012 it started to rain just after we had our picture taken on the way in. It continued to rain for most of the day and it didn't effect our time in the water at all. We maybe didn't have as long a day as we would have had in the sunshine cause we never really got time to sit on the loungers and relax. We were lucky that there were no thunderstorms that day so it didn't impact us going in and out of the different areas. We were lucky that when the family did the dolphin swim the rain stopped and whilst the sun didn't really shine it was nice a bright for the pictures.
We are going again in August of this year and hope that thunderstorms are not a problem - can't say I really care if it rains or not. Might even be better for me if it does as I tend to burn if I even look at the sun!