I have a 2009 VW Jetta Sportwagon TDI with a 6 speed manual and tow it 4 wheels down across the country.
Many VW dealers and info will tell you no... but they also tell you what the US tow ratings are for VW's. I started out with a 2005 VW Passat TDI wagon that was rated to tow something like 2000lb in the usa. in europe the exact same car was rated to two 3960lb.
Guess what? I bought a european hitch and a popup camper and towed about 3300lb with that car all day long.
So - bringing the point back to the 4 wheels down - I talked with the shop foreman at my local VW dealer (one of the largest VW dealers in the midwest) and he said it is 100% fine to tow it 4 down. When the trans is in neutral it will freewheel and there is no lube problems. You just need to leave the key in the ignition to unlock the steering wheel and turn the radio off.
I have a Blue Ox towbar and it works fantastic. In fact - I may even consider selling the car. Anyhow - it's a great setup and really easy to tow.
Go for it!