A big warship? But that is not a sailboat neither a small boat
It is crazy to think that a sailboat or any small boat can survive a major hurricane, I mean not near an hurricane but at the worst of it.
Miracles can always happen but they are miracles because they happen very rarely.
Big ships often fair worse than a small sailboat in extreme conditions. Whereas a large ship may span a few waves and beak her back, a strong, small sailboat would be much like a cork, if watertight.
I have survived 2 hurricanes at sea in sailboats.
The first was just west of Fiji, probably a high cat 1, but it was before satellites so it may not be a "full blown" storm in your mind. We were capsized 3 times and sustained a lot of damage, but she got us back to a safe anchorage, so I guess she was a pretty good boat, considering she was 65 when she went through it.
The second storm was in the western Indian ocean and because we were beating, we escaped the full force of the storm, but it was still 45 to 60 knots for 10 very difficult days as the darn thing chased us across the ocean. That boat was Brown 37' trimaran, which handled quite a few "heavy weather" experiences very well, including 1200 miles up the Red Sea in northerlies.
Once again, it would very much depend on the choices made by and the experience of the captain (certainly NOT the case in the hurricane (cyclone if you prefer) off Fiji, as I made some very bad choices, but as they say, "hindsight is 20/20"); good choices increase the survivability in any situation, especially at sea, in heavy weather.