I worked at a factory which built lapstrake "clinker" boats. Since then, I've been repairing them.
David H. is undoubtedly correct that about the lifeboat leaking that night. The nature of clinker construction is that it relies on the swelling of the wood to keep the seams watertight. All new boats will leak until this takes place. Titanic's boats weren't waterborne long enough to have swelled shut.
Clinker boats do dry out over winter in my part of the world. The old solution was to launch 'em in the spring and fill 'em with rocks and water so they would sink. After a week or so, the boats would be tight as new.
Dave G. is correct that you cannot caulk the seams of a clinker boat using 1912 techniques for timber construction. Pushing oakum into the seams would do little except drive the planks apart and loosen the clinched nails. Today, I use a polyurethane adhesive/sealant in the seams which not only waterproofs them, but also provides strength to the boat.
The tightness of the seams is a large part of the overall strength of the boat. This should have been considered in the scantlings of the design. A lifeboat does not have to be an easy boat to row or handle, so adding more strength of materials is acceptable than in a one-man pulling boat. Titanic's boats were new enough that drying out should not have created any strength problems with regard to launching them fully loaded. On an older ship where the boats might have been in their chocks for a decade or longer...????
One technique for "fixing" a leak that resisted swelling was to fill a can with sawdust (composted horse manure works better). A board would serve as a lid to submerge the can upside down beneath the boat. Then, the board would be removed and the sawdust would float upward, some being sucked into the opening where it would swell and staunch the leak. Sometimes.
Honestly, I do not believe that a summer in a hot storage room would have destroyed the boats or even caused serious weakness. Hot, dry conditions cause wood to shrink, but not rot. Consider the oldest boats in the world were preserved by hot, dry sand in Egypt.
Undoubtedly, Titanic's boats would have suffered open seams and cracked paint under such treatment. But, in the hands of a skilled boat builder they could have been made serviceable again. It is possible to "buck" the roves (clinched nails) and re-tighten the seams. Even a deteriorated plank can be replaced for far less cost than producing a new boat. In 1912 there were literally thousands of men trained in the ways of repairing boats.
My guess is that as soon as it was possible White Star disposed of the boats for a variety of reasons. They represented Titanic in any liability claims. And, they represented the result of unsafe navigation to the general public. Could they have gone to other White Star ships? Possibly. But, there were thousands of ships needing lifeboats in those days. Thanks to Titanic, there was quite a demand.
-- David G. Brown