I looked in to it myself a few months ago. It is possible. I was told the wheels would be stripped of all paint and lacquer in a chemical process, then the black coating would be applied finally the Diamond cut faces would be lathed at the end. I cannot remember the exact price now, but it was only around £100 give or take a few pounds, not near or more than £200. It will also take up to 3 days to refurb a wheel.
VW also do a Refurb thing where the company they use will provide a refurbed wheel to replace yours so you are not without a wheel at all while your wheel gets refurbed for someone else to have. To purchase a new rim from VW it will cost you around £640+ without a tyre. Just shy of £2000 for a set of rims without tyres.
So there you have it all the options I found. Except for the other option of a set of third party rims for less money. I am unsure of this option myself, but others on the forum have sworn by it.
The best thing i did recently was to coat my Austin Rims with GTechnq C5 Wheel Armour. I was a bit unsure about it until i coated my wheels and am more than impressed with the results afterward. My wheels appear much cleaner than my car after two weeks of driving around since the last wash. It's like the stuff repels dirt. It also reduced the appearance of the lighter hairline scratches. I have this patch of light scratches which looks like someone rubbed my wheel with wire wool on the diamond cut part. This has dramatically improved in becoming less noticeable since coating my wheels. I would heavily recommend this stuff to anyone with Austin Rims, or Diamond Cut wheels.