This isn't a square rig, but a bermuda rig. You don't go climbing on those.

And while the article doesn't explicitly say that sails was stowed, it does mention that they were only under sail propulsion once during the trip and that they started the engines to maneuver into the wind. While a (rolling? I don't know the English term) sail is somewhat exposed to the elements even while stowed, its rolled up fairly tight.

In short, I strongly doubt either wet sails or climbing crew contributed in any way to the sinking.