A story today reports that an autopsy on a kayaker whose body was recently found in Lake George found that he had drowned. The man wasn't wearing a life vest and apparently was not a strong swimmer. I don't know if he had a chance to grab onto the kayak, and kayaks, unlike canoes, can be hard to grab once you're in the water. They are sleek and slippery, and if they have turned over, do not offer an easy handhold. Wind could have blown the kayak away from the man in this case.
But every time a canoeist or kayaker drowns in a local lake, I feel the urge to repeat that canoes and kayaks do not sink. If you grab onto them — or even, especially with canoes, climb inside them — they will float, even when filled with water. If you aren't wearing a life vest (and you should be wearing a life vest), the canoe or kayak can save your life.
What you don't want to do, especially in the spring or early summer when the water is cold, is try to swim to shore. Distances over water are hard to judge. Even if you're a good swimmer, it can be hard to swim more than a few yards through choppy water, especially if you're wearing clothes. The cold water will make it hard to move. If you want to live, hold onto the boat. On a busy lake like Lake George, help will probably come soon, but even if you're alone on the lake, you can paddle with your hands while sitting inside the swamped vessel or kick with your feet while holding onto it and slowly make your way to safety.