It would probably work, but not pleasingly:
https://community.volumio.com/t/pi-zero-w-unresponsive/40847
https://community.volumio.com/t/pi-zero-wh/7883/6
https://community.volumio.com/t/how-to-connect-rpi-zero-dac-touchscreen/8032/2
For Pi2: https://community.volumio.com/t/3-5-inch-gpio-display-black-screen/46201/6
If you want to use kiosk mode, i.e. the Touch Display plugin, I would recommend to use a Pi3 or higher.