No, a heavy comet or asteroid cannot hit the Sun in the conventional sense. The Sun's immense gravitational pull prevents objects from directly falling into it. Any object that gets close enough to the Sun will be captured by its gravity and begin orbiting around it.
However, it is possible for a comet or asteroid to have a close encounter with the Sun, known as a solar graze. During such an event, the object can approach the Sun at a very close distance but will not collide with it. Instead, the intense heat and tidal forces from the Sun can cause the object to break apart or disintegrate.
If a comet or asteroid were to somehow collide directly with the Sun, the result would be an incredibly violent event. The object would be vaporized by the Sun's extreme temperatures, and the impact would likely cause a significant release of energy. However, due to the Sun's vast size and mass, the effect of such an impact would be relatively localized and would not pose a threat to Earth or the overall stability of the solar system.