If a 2001 Volkswagen Jetta's catalytic converter rattles and falls apart inside itself would that be covered under the voluntary VW factory extened emissions warranty even if you bought the car used?

AnswerYes, even used. See the EPA link below and show it to the VW dealer. Voluntary warranty extension from 8 years/80,000 (req. by EPA) to 10 years/120K miles.

But, if the catalytic converter has ANY visible damage the factory will refuse to honor the warranty. Since it can't be determined if the converter or the damage is the root problem. So before you spend the money to get the technician to determine if it is covered check the converter yourself.