Even though consumer drones cannot effectively eavesdrop on conversations, the question of audio recording law is worth understanding, because the same state privacy laws that govern wiretapping apply to any audio recording device, drone-mounted or otherwise.
Federal wiretapping law
The Federal Wiretap Act (18 U.S.C. 2511) prohibits intercepting oral communications without the consent of at least one party to the conversation. Federal law requires only one-party consent for oral recordings, meaning that a participant in a conversation can record it legally. A third party recording a conversation they are not part of without consent is generally prohibited.
State two-party consent laws
Eleven US states require the consent of all parties to a conversation before audio recording is legal. These all-party or two-party consent states include California, Florida, Illinois, Michigan, Montana, Nevada, New Hampshire, Oregon, Pennsylvania, Vermont, and Washington. Recording a conversation from any device, including a drone, without all-party consent in these states is a criminal offense. Even if the drone could hear the conversation, recording it would be illegal.
The public expectation of privacy
Conversations held in public spaces where there is no reasonable expectation of privacy (a public park, a street corner) are generally not protected under wiretapping statutes. Conversations inside a private residence or in a setting where participants reasonably expect to be private have much stronger legal protection. The same principles that apply to audio recording in general apply to any audio a drone might theoretically capture.
Note: Privacy law around drones is still developing. Several states have passed specific drone privacy laws that go beyond FAA rules. The FAA regulates airspace: state laws regulate what you can record and where. Check your state's specific drone statutes in addition to federal rules if you are operating commercially or in ways that may raise privacy concerns.