No, the Motion Encoder System is not compatible with TI-Nspire Lab Cradle.
Connecting a Motion Encoder Cart Receiver (MEC-BTD) to a TI-Nspire Lab Cradle (TI-NSLABC) will put the Lab Cradle into a diagnostics mode that can not be recovered without returning the Lab Cradle to TI for repair or replacement. Contact 1-800 TI CARES or ti-cares@ti.com
You can identify a Lab Cradle that is in this condition by the two LEDs alternately flashing red after pressing the reset button.