Yes, it is possible to program such function, in AN5444, chapter 5.2 you can find more details ( https://www.st.com/resource/en/application_note/dm00683267-iis3dwb-ultrawide-bandwidth-lownoise-3axis-digital-vibration-sensor-stmicroelectronics.pdf ). For battery operated applications specifically you may like to take care about the sensor power consumption and it is not the case of IIS3DWB (1.1mA current), we suggest then to enable the wake up function through dedicated lop power accelerometer IIS2DLPC where in wake-up set-up the sensor can run even below 1uA of power consumption. Once wake-up trigger occurs, an interrupt signal is send to MCU and MCU enables IIS3DWB to capture the data.
