No, in the absence of any external forces such as air resistance, the vertical component of velocity does not change in free fall. This principle is known as the conservation of energy. When an object is in free fall near the surface of the Earth, it experiences only the force of gravity acting on it. As a result, the object's velocity increases at a constant rate due to gravity, but only in the horizontal direction. The vertical component of velocity remains constant throughout the fall.
However, it's important to note that the magnitude of the object's velocity increases as it falls due to the acceleration of gravity. This means that the overall velocity vector changes because the horizontal and vertical components are combined, but the vertical component itself remains unchanged.