In this regard, is the AC pulley supposed to spin?
Yes the compressor pulley should spin at all times. If it did not then you would have a toasted belt. When the compressor engauges it uses a magnetic clutch mechanism which allows the compressor to pressurize the freon.
Correspondingly, what causes AC compressor to lock up?
The compressor is a pump that attaches to the engine of a car. It has the task of pumping a refrigerant gas, which is typically freon. Some of the causes for an automotive air conditioner's compressor locking up are improper lubrication, low coolant levels, and low-quality or incorrect types of refrigerant.
The clutch can seize, which permanently keeps the compressor activated; or it can break, which means the compressor will not be able to receive engine power. The only possible damage is when the pulley freezes it can cause the drive belt to break prematurely.