Could this sound information be captured on a camera?

Only if it shoots about 5k images per second or more. (see this and this) A bit less might also work, but legibility is already pretty limited at 2kHz Bandwith, but it’s probably possible to resynthesize some of the lost sound.

If so, then all the videos of cities at night might actually contain people’s private conservation’s in their homes, waiting to be decoded.

No, the sensors aren’t “high resolution” enough. For the work from the link they had to focus a telescope onto a special detector.