In the communications I have seen they see all CL models as Tethered models (2.4 Ghz throttle control or not) and do not need FAA registration. Because the handle is being used to control the model regardless if you have 2.4 Ghz you won't need an FAA registration. For Confirmation contact the AMA contact regarding this for the official word.
We have not seen any FAA inspectors at our flying site which has Drones, RC and CL flying.
And as a club we do not police if people should have or have FAA registration when they fly. Buder Park in St Louis only requires that you have AMA membership for insurances purposes. The Clubs and CD's (for official contests) only check AMA membership even for the RC and Drone events
Fred