I am going to assume that you have taken off the belt and are sure that exact pully is the one that is froze. So in that case yes there is a VERY strong possibilty that the water pump is bad. I have seen many water pumps freeze up and not leek. It's not real common but it does happen most of them leak. Once you remove it and try to free spin it you will be sure but I say since the belt is off and it's froze, your chances are almost 100% that the pump is bad. I hope this helps and good luck.
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