Of course you need to burn gas to produce electrical energy. And that's also how electricity produced by a rotating generator is "harvested". No one yet did anything to circumvent Newton's law.
So the question is one of overall efficiency. Which one's is higher, a Piezoelectric device or a rotating generator's. Also which is smaller, less expensive to manufacture, more reliable and less expensive to maintain.
Gulton and Piezo Electric products tried doing something like this 20+ years ago. The problem was the ceramic material would fracture over time with the flexing of the material. You need a polarized material that is not as rigid.
According to the article, and previous work, the energy is more-than free. You actually burn less gasoline. How does it conserve energy? Reduced heating of the wake and the airfoil skin. It reduces turbulence by absorbing the vibration energy on the skin. 30 years ago they talked about similar energy absorbing skins that allowed some fish and some submarines to go faster than a hard skin would allow. Very cool.