I know this does not cover the exact TDI you have but I found a VW service bulletin approving synthetic 5W-30 in TDI motors.
Subject: Synthetic Oil, Usage Group: 17
Model(s): All with TDI Diesel Engine 1996 ) 1999 Date: Feb. 19, 1999
Beginning Jan. 26, 1999, as announced in Warranty Service Circular V99-05, 5W30 synthetic oil has been approved and will be reimbursed under Warranty, when performing repairs or Free Maintenance for the models listed above.
When performing any service or procedure
which requires oil to be changed:
Always fill to appropriate level with 5W30
Be sure to utilize and claim correct quantity of synthetic oil depending on vehicle/engine class.
See Warranty Service Circular V99-05 for Part
No., quantity and ordering information.
Please advise your customers of this change
from mineral based oil to synthetic oil.