There is no technical reason for this to not work: When door moves the reflective tag gets out of alignment with the laser beam triggering the sensor. However depending on your location there may be regulations limiting remote operation to sectional garage doors only.
There is no need for direct support of Z-wave or Zigbee. Garadget uses WiFi for the radio protocol. Home automation hubs can communicate with it via IP network just like they do with many other Internet capable home automation devices.