The cork will float in water. There is no reason that the cork boat will sink in water unless you add dense and heavy material while building the boat. The reason that cork will float is because it is lighter than water.

Floating all depends on density. Density is defined as mass divided by volume. Any object that is less dense than what it is floating on will float, but if it is more dense than it will sink. If we float a cork boat on water, it will float because cork has a lot of air in it, making it less dense than water!

Yes, a cork boat will float, unless you load it down with so much stuff that it sinks, of course.