Piezo impact detection
A) Yes, it's perfectly possible to detect impacts with piezo's.

B) No, you're not going to use them to detect nerf gun hits.

For piezo's, the problem of distinguishing between noise (vibration, etc) and an impact is (for relatively gentle impacts) a real issue. What you need is a very hard, short impact process, and I'm afraid nerfs just don't fit the bill. Add to this the extra impact-like signals you'll get from things like footsteps, and you're looking at a pretty hopeless situation.

You're free to try for yourself, but be prepared for frustration.