A sit in kayak without bulkheads can sink, but they almost always have enough foam to keep them on the top. They can easily sink enough so that a pump won't do anything, though. If a boat doesn't have bulkheads, float bags are a must for anything further off shore than you want to swim with a boat that is fully loaded with water.
Again though, this is why I strongly recommend taking a new boat to a pool session and testing all these things out in a controlled environment before something bad happens out in the middle of the bay.