He can but the umpire, in his descretion, probably won't give the batter first base
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No you don't have to. The pitcher will get upset and the batter will be stung but if you are going to be hit and you don't move, it is considered hit by pitch.
The only time I have ever thought it happened was in softball, where a pitcher just tells the ump to let him take the base. No need to throw the balls. (thats what she said)