Yes, 6600 is 10 speed as is Tiagra, so you should be okay. The only thing I'd be concerned about is whether the cassette and the rear derailleur are compatible. If the cassette you're fitting is a wider-range than the old one, the derailleur might not be able to cope with the extra teeth unless it's a medium or long cage. What ratio cassette did you have, and what are you replacing it with? Also, do you know if the derailleur is medium or long cage?