The boat in question was a 15 meter long oak on oak boat. It lasted 2 winters for 2 homes with a fire stove, and we didn't even burn it all.
There's an amazing amount of wood in a boat, particularly around the keel. The framing, keel and other structural elements are made of really heavy timber. On top of that good wooden boats are (were..) built of slowgrown oak that is incredibly dense. One large piece would last for 6-8 hours in my stove and give off a lot of heat.
It doesn't seem unlikely to me that a 25-30 meter boat would last for 15 years if you the goal was primarily to keep the fire going, only getting it really big/hot when needed.
Well played, sir.
Some quick Googling puts the weight of three masted schooners at 300-400 tons; a cord of firewood weighs 2 tons, so that's between 150 and 200 cords of firewood. Some of that was reused in the escape-raft and some of it was presumably unrecoverable, but if they were able to recover 25% of it, that's somewhere in the neighborhood of 50 cords of firewood, or around 3 cords per year of the 15 years.
3 cords is a reasonable amount for a house to use for heating in a heating season in the US. That's less than a year, but you're probably burning it faster than you would if you were carefully husbanding a fire and occasionally using it for cooking or warmth or light.
So it's totally plausible (which is good, considering it happened), but the numbers are close enough that I couldn't guess whether you'd expect the average shipwreck in similar circumstances to run out of wood after ten years or have enough for a hundred, without having more information about the burn rate in this particular situation or how much wood they actually were able to recover.