Sternone,
Both the instructors at my school have bose X, and I'm training in a C152 - so I doubt there is any problem there. I can hear them OK (in borrowed denali's) and they have no probs with ATC.
However, I can't say that I've ever noticed the ANR box, so they may be using them as passive only? I'll have to ask to see whether it's because of compatibility or choice (don't want to hear the student wittering on!).