Does the 2001 Audi S4 have an interference engine?

Yes. The Audi 2.7T twin turbo and 2.8 NA V6 are interference engines. The later generation V8 is also, but I believe they have chains. The recommended interval for changing the timing belt should NOT be ignored. If the belt breaks or slips you will have valve damage and more than likely piston damage as a result. At the time of a timing belt service, be sure to replace the water pump, and TB tensioner as well as the belt. All of these things can be accessed or are easily accessed when doing the belt.