Does Gibbs' team use earwigs

yes there are many types of such devices; some corded to a radio and some wireless through their cell phones.
海军罪案调查处 LA uses wireless and 海军罪案调查处 used wired.

They did in the episode which featured David Keith as a Navy captain whose wife and blind daughter had been kidnapped. The earwig provided an amazing means of communication with the captain, who was under surveillance in his office. (The captain himself turned out to be the bad guy, but that has nothing to do with the earwig.)