Cockpit drain through hulls should be left open for obvious reasons. All sorts of problems can crop up if you allow your cockpit to fill with rainwater....
Your bilge pump should be direct wired to a battery and function whether or not your batteries are "switched on".
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)