That depends on what your goal is.
If you want to reduce pain and inflammation so you can get back to what you were doing without truly healing, then yes. But do you really want that? If what you really want is full and complete healing, then the answer is NO! (By the way, no judgment here, it really is a choice)
Ice works by reducing the blood flow to the area thus limiting the inflammation possible. The swelling will go down, the pain will be numbed by the ice, and you will feel better. Sounds good, right? Inflammation is the first stage the body uses to heal. When you disrupt that stage, you make healing more difficult, and can turn an acute injury into a chronic condition.
Inflammation creates an increased blood flow which brings white blood cells to the area allowing the body to clean things up. It also shunts away all the damaged cells and other debris. The increased swelling acts like a splint to reduce movement. The pain itself tells you exactly how far you can move and what activities to avoid. All of these processes allow you to heal. When you experience the pain, and as it lessens day by day, you will be able to move more and more. That’s a good thing to do because it’s the movement that allows the soft tissue fibers (like scar tissue) to line up in the correct direction. Then the scar tissue can bring the healthy tissues together again, and you will heal.
Icing the same injury prevents all of this. Taking ibuprofen also does. Then what you have is a crippled attempt to heal, which doesn’t produce the same benefit, and which won’t allow for complete healing. Additionally, you may reinjure yourself, because by not feeling pain, you can do more than you probably should be doing. While this may allow you to get back to your job or your sport more readily, there will be long-term consequences.
So what do you want?