Well, it seems that you have little knowledge about blinking. As you can see, we ordinary people blink frequently from time to time, and the main purpose of blinking is to keep your eyes moist, because constant exposure to the air will lead to dry eyes, which is not a good sign of health. Of course it would damage your eyes, and you will automatically shed tears. Actually, you cannot hold more than 2 minutes, trust me.
Yes, it will damage your eyes if you don't blink. The movement of blinking is the natural behavior which will be happened in the unconscious way. If you try not to blink, you will find that your eyes may lose the water and become dry. The blinking eyes will keep the eyes at the moisture state. It is necessary for our eyes to work normally.