Once the wood swells, you bail the water out and it should float.
Although these guys seem to think the wood they were working with was OAK, maybe the part they tested on the original was oak, but the rest of it may well have been birch planking. It's much lighter, exceedingly water-tight, and flexible enough to allow the caulk to work correctly.
Now, commentary about "Biblical" meaning "real old", the Bible has parts that are clearly from the Bronze Age ~ and so was the original boat. They are contemporaries. However, if you want some "real old" wooden relics you need to check out frozen tundra in the far North. Wood can and is eaten by everything you can imagine. It's rare to find worked plank that is really really really old ~ although recently someone discovered some fire hardened point sticks that may date back to the last interglacial! (that'd be more than 110,000 years ago).
'So make yourself an ark of cypress wood; make rooms in it and coat it with pitch inside and out.'
Throw in the fact that our fore-bearers sailed/navigated? to Crete 100k plus ya.
You can do things for a hobby. But, if you life is in on the line, ya learn quick.