Look up the recent demise of the HMS Bounty- a replica ship which was taken to sea to avoid damage in port due to a hurricane and instead sailed right into it.

Would any naval battles have taken place during storms?

Just looking at the practical aspects of this I would have to say no, or at least only as an act of desperation. Manning and firing a gun on an open deck would be nearly impossible. Opening the gun ports on lower decks would almost certainly end badly. And even if you could get a shot off, as the ship pitched and rolled, odds are that it would hit nothing but water.