No, if an object is thrown downwards at a speed faster than its normal terminal velocity and is given enough room to fall, it would not eventually slow down to the terminal velocity.
Terminal velocity is the constant speed that a freely falling object eventually reaches when the resistance of the medium (such as air or water) through which it is falling equals the force of gravity pulling it downwards. When an object reaches its terminal velocity, the net force acting on it becomes zero, resulting in a constant velocity.
If an object is initially thrown downwards with a velocity greater than its terminal velocity, it will continue to accelerate due to the force of gravity. The resistance of the medium will also increase with the object's velocity, but it won't be sufficient to balance the force of gravity. Therefore, the object will keep accelerating until it reaches the ground or encounters another force that affects its motion.
Keep in mind that the concept of terminal velocity applies specifically to objects falling through a medium like air or water. If the object is falling in a vacuum or a medium with negligible resistance, there would be no terminal velocity, and the object would continue to accelerate until it reaches its destination or encounters other forces.