Like a lot of fishing boats, Boston Whalers come to mind, the buoyancy isn't built into the bottom of the boat, it's built into the sides. I think if you removed the bottom, you'd be shocked how high in the water the vessel actually sat.
Check out a Freeper's post #73 on this thread. It's a funny story that gives great anecdotal evidence about how buoyant these things really are.
Oddly enough, the best thing the Navy and this skipper have going for them is time. The longer it goes, the more fatigued the pirates will become and the more likely the chance there is that they'll make a mistake.
From a guy who did this for twenty years, there aren't any good military options available on the open sea with a ship this small. As soon as things start to go down, the hostage would face a significant chance of injury or death.
Oddly enough, the worst thin this captain has going for him is the steamy baking heat of up to 100+ degrees Fahrenheit. And after being submerged in the extreme very salty water, his body must feel dry and like scale on him. No A/C on the lifeboat and the scumbags are used to that kind of weather condition!!!