Yes, paintballs will always hurt, if you cannot feel them under your clothes, you are technically cheating.
Although it hurts to get hit with a paintball, you can't wear extra padding because the point is for the paintball to break. Experienced players feel the paintball much less because they are accustomed to the pain. If your adrenaline is pumping really fast during the game, you are likely to not feel the shot too much.
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No it won't hurt, but wearing that armor will slow you down and the slower you are the more you will be shot. Armor only protects your chest and sometimes your back. If your a good player you shouldn't be exposing that much of your body long enough to be shot and should have no need for the armor. I am the captain of the Bullit Paintball Team and have never seen a real need for the body armor. Being shot doesn't hurt, unless it's the back of your leg (which armor doesn't cover anyway). It's best not to spend the money on the armor and put it into upgrading your gun.
Paintballs will always hurt, but an added layer of protective clothing will reduce the sting roughly a fifth or so. With only a thin shirt, paintballs at an average distance sting as much as a thick rubber band snap to the back of the neck. If you wear too much however you will overheat and be very slow moving, which will get you shot more often. It also should be noted that "armor" or specifically padded clothing is looked down upon by most players, and may cause then to shoot more intensely at someone wearing it.