The case cuts down the noise. It also cuts down the sound. There's an accessory door for the case (the round one in 'AKA-RD1') that will help - it has thin windows over the mics. You could wrap the whole thing in a 'Dead Kitten', made by Rycote or Rode for a professional solution, or DIY a little moustache? But keep the whiskers out of shot (lens-hood ?).
Being that the camera will be inside the waterproof case in such an event, there is little to no chance that wind noise will be recorded. When the camera is inside the waterproof case, the microphone on the camera is covered by the case to protect it. Please see our eSupport website for further details; http://www.kb.sony.com/selfservice/microsites/search.do?cmd=displayKC&docType=kc&externalId=C1031761