I would definitely wash it off. Not sure what the rationale would be for leaving the brine on. It certainly wouldn't help the flavor at all.
After you are done brining, you want to give it a good rinse in cold, running water to make sure you get rid of any and all possible salt deposits on the surface. Also, the brine water can get pretty murky - you don't want that stuff on the surface of the meat. Once you have rinsed it well, if you want to dry it, pat it with paper towels and let it air dry in the fridge (for chicken or turkey, air drying helps immensely in getting a crisp skin).