While I've seen this story online, I have a lot of doubts. It seems like a conflation of several stories that grew taller over time. What is true is that several crewmembers of the West Virginia survived for several days, although they weren't in an air tight compartment but rather climbed up on steam pipes inside an air pocket. From CAPT Homer Wallin's (later Vice ADM) recounting of the salvage of the West Virginia:

Human bodies were handled as in California and were taken out almost unknown to the working parties. Sixty-six bodies were found throughout the ship. Several bodies were found lying on top of steam pipes which were in the air bubble existing in the flooded areas.

The rescue of survivors that were discovered by tapping actually happened aboard the Oklahoma and the Utah. Wallin provides a description of the rescue of the men on the Oklahoma:

At first they tried to gain access to the inside of the ship by acetylene torch, using it in locations free of oil and water, but found that the fumes from oil and the cork used for insulation were deadly to the men who were trapped in the locality. Accordingly, they thereafter used compressed air and corresponding tools which were furnished by the Navy Yard and various ships, including Maryland, Argonne, and Rigel. The Navy Yard and ships concerned provided submersible pumps, sound powered telephones, and air ducts for ventilating purposes.

Soon the trapped men were located in the vicinity of frames 131, 116, 78, and 22. The men were all near the bottom of the ship, which at that time was partly visible above the water level of the harbor. It was not until 0800 on 8 December that six men were rescued, and at 1100 eleven more were brought out. Five more were released at 1400 and eight at 1600 on that same date. The last man was not rescued from Oklahoma until 0230 on 9 December. All were in good condition except for lack of sleep, food, and sufficient oxygen. Some of the thirty-two men were dependent on an air bubble for sufficient air. Of course the air bubble gradually disappeared and water rose as soon as an opening was made in a compartment. A watch was maintained on the hull of Oklahoma until 11 December but no further signs of life were detected.

One sailor, John B. Vaessen, was rescued from the Utah by crewmen from the Raleigh cutting him out of the bottom with an acetylene torch. He called the sparks from the torch coming through the hull, "the best shower I ever had."

If they were aware of the trapped crewmen on the West Virginia, every attempt would have been made to rescue them, but tapping on a steam pipe deep inside a battleship would probably not be easily heard from outside. Rescuing sailors was a top priority along with preparing for the next possible attack. That being said it would not have been easy. Fires burned for 30 hours, and the West Virginia was severely damaged by possibly seven torpedoes, a couple of which had entered through holes created by earlier torpedoes. They originally thought it would never sail again, and may have only been saved from capsizing by being pinched against the bottom by the Tennessee until it could be righted by counterflooding.