They used to do it 20 years ago when the tweeters which had some power handling to speak of hardly had good dispersion.
If you think your system lacks HF, yes you can try out a piezo, its so cheap anyway.
Piezos have impedances in the hundreds of Ohm. You should run a resistor across it in the order of decades of Ohm. Then feed it with a .1 to .22 cap on the plus terminal.
3 things are your playground so to achive good integration.
a. The lesser the resistor the less the dB.
b. The smaller the cap, both less dB and higher cutoff.
c. Positive and negative polarity test to hear for best addition with your tweeter.
I would start with a 33 Ohm across, .22uf, and negative polarity on the piezo.
Good lack.