Is it actually possible to hear a tendon tear?

Yes. It can happen. Sound waves travel in the body as well, so some people can hear these things when they happen, just like people hear their own heartbeat.
Absolutely. I have had patients tell me that their tendon tears have sounded like a gun going off, a loud pop, a snap, etc. These tendon tears have included rotator cuff, pectoralis major, triceps, biceps, hamstrings, quads, patellar, and achilles.