Good morning XXXXXXXX,
The clutch does come with the compressor. When an a/c compressor is ordered by the dealer from VW it should come as a complete unit. I have seen techs struggle with figuring out why the a/c does not operate on your model of Passat. The a/c compressor clutch is a big magnet that is powered up, locks into place and turns the compressor. The clutch receives an activation signal from a relay. The relay needs to see an input signal from the a/c high pressure switch through the vehicle interior temperature sensor. If the dealer is saying that they replaced the compressor and now it needs a clutch the tech working on the vehicle is probably not sure why the system is not working. Either way, before ordering a compressor the operation of the clutch should have been checked and confirmed as being correct, this is generally a step taken as a new compressor is an expensive component.
Good luck and I hope this information helps you resolve your a/c concern. Max
VW Shop Foreman
VW certified lead technician, ASE certified Master Technician, 10 years experience