This depends on the company procedures but as a rule of thumb, deactivation requires a minor modification/change authority that would have to permitted by the engineering group. An inoperative component can only be deferred by MEL.
If the aircraft was fitted with CPDLC but is inoperative, ask to see the minor mod paperwork for the deactivation, if it was carried out as part of a larger bill-of-work (check) there may not be an obvious entry in the tech log.