Yes that is normal. It should only engage when cooling, (engine running) if it short cycles it could be low on refrigerant. If it spins freely the clutch is most likely OK. Are you sure the noise is coming from the compressor? Is it only noisy when the air or defrost is on?
If the compressor is bad you will have to do all the steps 47 stated, plus flush out the lines, evaporator, condenser with a flush solvent. You will also have to remove the metering device and replace it. You are not able to flush through the metering device.
I would not just consider replacing the dryer, I would do it. You are going to have a lot of work into this to get it running again, no sense in trying to cut corners.
I don't know what state you are in, but I would love to be thinking about air conditioning right now. Current temp *18f, temp this morning when I got up -7*f
edit; I see you are from North Carolina, missed that at first.