The FCC is responsible for monitoring the use of the airways and enforcing the various laws. This includes commercial radio, TV, telephones, amateur radio and all types of radio communications outside of military usage. Currently, the agency is woefully understaffed as any licensed amateur radio operator can tell you. There are several unlicensed stations (termed Pirates) operating that the FCC has failed to do anything about for years. Unless it presents a clear and present danger to life, as in interfering with first responder communications, the chances are slim that they will do anything about any violations, and that is without adding the responsibility of monitoring drones.
That isn't to say the FAA might not get involved, but I believe their staffing problems are in similar disarray and I doubt they will be too excited about chasing "illegal" drones.