Is the LEGO Mindstorms EV3 brick waterproof?
No, the LEGO Mindstorms EV3 is NOT waterproof. Any electronic product that is capable of being immersed in water will clearly state in the packaging/manual the level of water protection provided. This may be in the form of an IP Code:


  Ingress Protection Marking, classifies and rates the degree of
  protection provided against the intrusion (including body parts such
  as hands and fingers), dust, accidental contact, and water by
  mechanical casings and electrical enclosures.


Source: http://en.wikipedia.org/wiki/IP_Code

However, it is possible to contain the EV3 brick within a waterproof case, there are already many cases available suited to Smartphones, Tablets, Cameras and other Digital devices. 



If your remotely operated underwater vehicle requires some form of propulsion (perhaps from a propeller powered by a EV3 motor) then you may required to make some alterations to the case. Any physical alteration will compromise the waterproofing and safety of the protective case. Do so at your own risk.