There was a television programme done in he UK where they built a wooden submarine and submerged it. It didn't leak, it worked like a charm. They were recreating it to disprove / prove a historical myth I think. They even had a mechanism to make it go up and down.
Only catch was the air in the submarine became toxic very quickly, you'd suffocate after just a little while. Of course if you made an electrical wooden submarine with an air filter and what not, sure, I guess it could work. But why?
(Oh and to clarify this took immense workmanship, you could not make one yourself at all)