My wooden Bayraider 20 has no seals on the lockers, and drains at the bottom of the lockers.
I assume this is so that water can come and go from the lockers if/when the boat capsizes. I suspect that with sealed lockers the boat would float too high to get to the centerboard which would be a problem.
I do enough coastal sailing that I want to know that I can right the boat with or without ballast if necessary. As a result I am happy to give up waterproof lockers.
Everything in the lockers is waterproof. I use the rather expensive but foolproof Watershed drybags for anything that must stay dry such as clothes, sleeping bag, matches and phone back-up charger. I squeeze as much air out of them as possible (they have a valve), both so that they are as small as possible and also so that they add as little flotation as possible.
My electric engine is waterproof, as is the battery which is on an extension cord in the locker as far forward as I can place it to keep the weight out of the transom.
In heavier weather I am also waterproof in my drysuit!
As has been mentioned, there is a long string about waterproofing the lockers. To me it seems altogether better not to need to, as it is unlikely to be successful in the end anyway. After all, we are sailing in small boats!
The original point was that rainwater filled the cockpit which went into the lockers. Very little water will go into the lockers before it comes out even with the boat listing.
I have found that my boat can sit for weeks on her mooring in Devon rain, and drain perfectly so long as the ballast tank is not full.
I would not leave the cockpit drains closed. After only a week away recently, I returned to find my tender on the mooring with only 3 inches of freeboard. Fortunately my hand powered, large capacity, water ballast bilge pump has an intake hose long enough to go over the side of "Pippin" and into the tender. It was pumped out in about five minutes, and I was a lot warmer for the exercise!