I've found that the piezos react to regular electric strings similarly to how an acoustic undersaddle pickup would react to electric strings: poorly.
The compromise I've found is monel alloy acoustic strings - they're close to acoustic tension but are fully magnetic and work perfectly with the regular pickups. Martin Retro monel 10s come with a wound third, and I've found that makes the models sound more authentic and reduces the ghost fret noise a bit.