Depends. If you can throw something faster than it's terminal velocity then it will exceed it until the air resistance will brake it.

Imagine throwing a balloon downwards. You'll have to exceed it's terminal velocity just to move it, and it also quickly stops going faster.

Same thing happens to other stuff. It can move faster than terminal velocity, but the force you apply will not be permanently added to its speed.

Imagine throwing a bowling ball downwards. It has a high terminal velocity. You can't throw it that fast. By throwing it downwards, you are helping it achieve terminal velocity, but it doesn't exceed it when it reaches it.